"I could do one that just makes something glow? The reason it takes so long is that all the runes have a bunch of different meanings, and you need to set them up to cancel each other out so you're left with only the meanings you want, and then draw the diagram really precisely. I'll need a sheet of paper about this big," hand gesture of about ten inches, "and something to write on it with, and some more paper for working out the math, and ideally a ruler and a protractor if you have any."

Nod. "Yes, of course, I'll work on getting you all that." 

It takes the guards a while to rustle up all the requested supplies, but they do eventually hunt down a protractor and ruler as well as pen and ink, and then the mage leads her down some stairs to a stone-walled windowless room, with an oddly dampened feel. She lights it with a mage-light hovering at ceiling-height. 

She wonders if the protective magic on this room would actually help at all if someone other than her failed at runecasting in here, but there's no good way to find out. She braces the paper against the most convenient flat surface and does algebra and then geometry. It's not very interesting to watch.

It's in fact very boring to watch! But the mage is very dedicated to her job here, and she leans against the wall and watches, Othersenses on alert, checking when any of the paper and math on it starts to become magical. 

The runes start being magical when they're written in the actual diagram structure instead of on the scratch paper, but very--quietly, like they're dormant. 

Eventually Margaret says, "I'm done. I can try making the pencil glow now."

"Sure. I'm watching." The mage leans forward, quietly hoping to herself that the payoff is worth it for all this standing here, her feet hurt. 

Margaret sets her pencil down on the diagram and says some incomprehensible stuff and the pencil starts glowing, all over with a uniform green light. To mage-sight, it looks like the runes stop being dormant, dump a bunch of magic into the pencil (where it remains), and then become as utterly inert as a child's drawing.

"....Whoa," the mage breathes. "I'm - I don't know where that energy came from -" She would ask Margaret to do it again but she's not sure that would actually help. "How long will it keep glowing for?" 

"I did one of these over a year ago and it's still going."

She'd mention the infinite electricity artifacts, but one, she doesn't know that they even have electricity here, and two, she's still nervous about explaining how much she can do and why.

"Hmm. May I borrow that pencil for a bit to, er, show some people? I can return it to you after if you want." 

"Sure, go ahead." It's not even Margaret's pencil in the first place.

"Could you give me a really quick overview of what sorts of things the other runes in your book could do?" 

"Hm, it's pretty freeform and there are definitely things that I don't know are possible--manipulation of heat and light and sound, including seeing things far away, and teleporting and making spaces bigger, and healing and other biology things, and," yup no Tantara word for electricity per se--"uh, controllable small amounts of lightning, and detecting other magic, and at least one person could walk through walls but I've never tried it."

The mage scribbles down some notes. 

"All right, I'm going to take you back to - hmm, somewhere you can make yourself comfortable, we might be asking you to wait a bit. Have you eaten recently?" The mage leads her out of the Work Room and back up the stairs. 

"No, I haven't." She went from breakfast to a while of being busy in her workroom to being too confused and scared to consider food, but now that she considers it it's subjectively a long time past lunch. Also she's probably going to turn out to be interdimensionally jetlagged. "By the way, what time it is here?"

"Late afternoon. We'll get you settled somewhere and bring you lunch, all right?" 

She takes Margaret back up to the waiting area, and then has a long conversation with the older Guard on shift, in the foreign language. It sounds as though finding Margaret somewhere comfortable to stay is complicated.

Eventually the mage comes back out and walks with her, out of the Guard-station into the middle of a bustling but visibly very very low-tech city - the road is cobbled with ditches for sewage along the edges, the people are on foot or occasionally riding horses, there's no sign of electric lighting - and leads Margaret across the street to what seems to be an inn.

(Another of the Guards follows, keeping a discreet distance but obviously intending to supervise Margaret.) 

"I'm sorry, no one here is likely to speak Tantaran," the mage says to her, after talking to the innkeeper and bringing Margaret up to a room. "I'll have them bring you food, and if you need anything else you can - mime, I guess, or I can tell you how to ask in the Predain tongue for food or water and things...?" 

Oh no, sewage ditches. They probably aren't going to have toilets and showers like she's used to, either. Ugh. (She tries not to let any of this show on her face; it's not their fault. Maybe she can invent indoor plumbing.)

"Learning a few words of the local language would be good; I'll need to learn it eventually and I'm good at languages."

Then the mage will stick around for a few more minutes, even though she seems to be quite impatient at this point, to give her a list of basic phrases and let her repeat them back a few times to correct pronunciation. 

"Thank you! Sorry for taking up so much of your time; I'm sure you didn't have 'help extremely lost person' on your schedule today."

Once the mage is gone, Margaret saves this location over the earlier one and tries teleporting home again. Still nothing. She eats her dinner and flops on the bed and misses home and wishes she felt sure enough she wasn't being watched to transform.

The guard stays outside her door, though he doesn't watch her directly. No one else bothers her that night, except a chambermaid coming in to empty her chamber-pot and ask if she wants a bath (miming it, but also the mage taught her the word for 'bathing' so she can recognize that.) 

She wants a shower and to go home "Yes, bath, thank you."

The bathing-room is unimpressive but the copper tub is clean and the maid does all the work of toting buckets of hot water for her, and gives her a fluffy towel and soap that smells reasonably like normal soap, and then mimes to ask if she wants help scrubbing her back. 

She can scrub her own back, thank you. Being nude in front of a stranger and not having any money to tip her with are new and exciting vistas of embarrassing but at least she's clean. She goes down to the common room to get some language immersion. Hopefully "selling magic items" is a reasonable way to get by in this society and she'll be able to find her feet while she works on a spell to get home.

It's a big enough city that people are fairly friendly and curious about the exotic-looking stranger, rather than mistrustful, and when she manages to get across the concept of 'selling magic items' they seem to recognize this as a known thing, and smile and bob their heads. She gets some language immersion. The guard watches her from across the room, but isn't very intrusive and seems apologetic rather than hostile about the whole thing. 

After that she can go to bed. 

...Rather early the next morning, there's a loud knock on her door. 

Probably the mage again, or someone from the same police department/army/she should really figure out who is detaining her and under what conditions they would stop. She opens the door.