BLUE TONGUE SKINKS

First off, I know lizards don't really feel happy (though I am curious about the research on that or any kind of lizard emotions, I haven't found any, if anyone knows I'd appreciate it)

I got my BTS about 3 months ago. I started handling him after a few days because he seemed already domesticated at the store. He's always been a little grouchy and huffy, but never bites me. However, for the last month or two I kind of stopped handling him because I've gotten busy with schoolwork, and I feel a little guilty. I want to be a good lizard parent, but he's just been sitting in his tank with nothing to do. is there a good rule of thumb for how often I should (or shouldn't) handle him? Any good things to keep him entertained, like toys or something, in and outside the tank? My go-to is just to sit him on my head and watch a movie with him. I've been putting it off in case he pees on me. :/

Any tips? Much appreciated

Rearranging the tank can be a form of enrichment. Add some moss or a new hide if you're able. I've seen some placing food inside wiffle balls to keep them occupied for short periods. There's no rule of thumb for how often you should remove them from the enclosure. However, most are completely fine being left alone.

Hi there, I agree with rearranging the enclosure. They love that. Also adding in new tunnels or caves is a favorite as well. You can hide treats around the enclosure for them to find (fruits). They like that. As far as handling every skink is different. Some like to be out and about and others really don't like to be handled. My Merauke would sit and chill with me all day if I let him. My Northern, well he is all about moving and finding a place to escape. I can't trust him at all to be out unattended. So you just have to judge your own reptile. The other big thing is making sure they stay warm while outside of the enclosure and don't get to cold.

Yes, please limit out time when temps are low. It does nothing to benefit them coming out of a 90 degree cage into a 70 degree room, and if they seem cuddly it's because you are warm and they are cold. Please remember they are reptiles and not dogs.
A note on re-arranging... all are different there too. Mine absolutely hate any type of change, and will not settle down for days if I attempt it. All with the exception of one or two, who always hide anyway regardless.