Earlier today my boyfriend picked up a young, underweight Halmahera skink. I was suspicious of it's condition but the guy at the show says the last time it ate was three days before, and it's been eating pinkie mice and crickets (ugh, really?). I'm hoping that this is simply a case of neglect rather than parasites or disease. (I mean that in the best way; because now it'll never be neglected again!) There's some evidence of a rough shed not too long ago; it's face looks patchy as if it was half-shed and there was some skin still on it's toes.
We set it up in a 20gal long tank since it is so young and small. We have a nice reptile-specific 55gal long tank for it when it's big enough to easily make the distance. At first it hid in the regular hide for a while, and I can't blame it! I set up some damp terrarium moss in the plastic container it came in and cut a corner off to make an impromptu humid hide to make the last bit of shedding a little easier. It did sit in the humid hide for a little bit, and then finally came out to explore.
The water dish is flat and long- I chose this one so it could lay down in the water as a second option to ease the rest of the shed. The skink immediately drank a ton of water upon discovering the dish, and it's been sitting in the water for over an hour now. I'm assuming it was dehydrated, but I'm glad it at least shows an interest in drinking.
We put in a little plate of scrambled egg and minced green peppers to see if it showed an interest in food. It's our Irian Jaya's favorite, so we hoped that it would incite a hunger response. No such luck. The skink saw the food, went right up next to it, but hasn't sniffed/licked it closely, and went back down to the water dish. My uneducated opinion is that it's used to delicious, fat little pinkies and hasn't been exposed to anything else yet. It might also be full from drinking so much to overcome dehydration?
Oh, and this is common sense, but figured I'd keep your minds at ease- it's totally quarantined from the other reptiles.
Pictures (sorry for the quality, I took them on my phone)

This is a fuzzy shot but you can see his little hip bones


In this pic (and the ones below) you can easily see the spine and the patches on his face.




So these are the questions I have:
I know scrambled eggs aren't much healthier than pinkies. What should I try feeding from here on out? (FYI, this isn't the only thing we feed the skink we've had- he gets a varied diet of greens and proteins; kale, collard greens, peppers, spinach here and there, cat food to interest him in greens, etc.)
Should I keep food in there daily, just in case it does show an interest? Or try every 2-3 days?
How long should I try to feed naturally before resorting to syringe feeding? (I have fed leopard geckos via syringe before, so I do have some experience, albeit not much. I'm in no rush to try it if I don't have to.
It seems alert as far as I can tell. It is only the first day home, so I'm not messing with the skink or the tank any more than I had to (to put in the humid hide and the food only). I realize it's stressed so I'm keeping a careful, but distant, eye on it.
Is there anything I'm doing wrong? Or something else I should be doing? I'm looking into vet office hours as we speak.
Any advice will be much appreciated. Thank you for reading!