All the normal FJ things body and body mechanical wise, i think these have been covered pretty extensively on here so I'll skip them.
HJ specifically, I'd watch out for excessive smoke, either white/blue or black. There's a hefty puff on startup that you can ignore, it's just their nature. Thick black smoke usually means the owner has messed with the fueling (too much fuel = excessive smoke and too much extra heat = potentially a ticking time bomb for a VERY expensive rebuild.)
A pyrometer install is usually a good sign that the owner has taken care of their truck, or at least paid attention to how they drive. It's possible to do engine damage with EGTs getting too high before you see any sign of high coolant temps. Of course take it for a drive and make sure the coolant temps don't get too hot too. But these trucks have a massive coolant volume so it takes a lot to get them up above the gauge.
Also make sure the HJ actually contains a 12HT, the 2H also gets the HJ designation and you'd be in for a nasty surprise if you were expecting to go faster than about 45 from what I hear
If the owner will let you, pull off the rubber elbow piping that goes to the turbo intake and check the turbine shaft for excessive play. Can't remember the exact specs off hand, but do a search and you'll find plenty of info.
Check that the glow screen is functioning properly. My cruiser will start right up after glowing even well below freezing as long as I've got the choke set right. If it's not too cold, any hesitation on startup would be a warning sign. A 24v starting system is nigh instantaneous - mine starts faster and easier than my girlfriend's brand new Subaru.
Make sure the electricals are largely untouched, finding the correct wiring diagrams is tricky and unraveling some rando's bodge job is not fun at all...I'm 5 years in and I'm finally most of the way through restoring my wiring to fully working order.
If you're looking at a PTO equipped model, make sure it engages and turns freely - but only start it with the actual exterior lever disengaged. It's a strange beast and if you don't know what you're doing it can be quite dangerous to both you and the cruiser.
Check the sunroof for leaks. My gears were stripped out, but it wasn't leaking so I just ran a solid bead of silicone to make sure it stays sealed. You don't want your high roof rusting out, it's not like donor vehicles abound.
Shifting should be smooth and easy, although the h55 is a little bit notchy when cold so don't judge until you've got some heat in it.
Make sure your 4wd (hi & lo) is actually engaging, and check the locking hubs. Oem replacement hubs are available in the US though so not a deal breaker if they have issues, it's a pretty cheap and easy (although messy) fix. The vacuum 4wd system is way more of a pain, and i think I remember reading that it's possible for the light to indicate that it's on without that actually being true.
Make sure the alternator is putting out solid consistent voltage. Replacements are expensive, although usually a good old school alternator shop can rebuild them. I'd check with an actual multimeter, the gauge is consistent but not always correct.
Of course, take it for a drive. If you let revs fall pretty far after shifting and then ease on the gas you can really feel the turbo engage. Don't expect to get pushed back in your seat by any means, but you'll know when it builds boost. If that feeling is missing, walk away as either the turbo is seized, or already vomited it's internals all into the engine. Before turning up my boost (super easy, highly recommended mod), i could hold 55-60 all the way up and down I70, so if it's having a hard time on the highway, something's wrong.
I'm not sure where you're located, but make sure you do your research for what they will and won't allow you to register as far as originality, etc. Here in CO, they require all emissions equipment to be present and original, with a few exceptions for NLA parts. The guy in charge of it here is super knowledgeable and actually quite friendly as long as you treat him with respect and don't try to pass your coal rolling 1000+HP/tq Cummins as original equipment. He sat on the phone with me for 20-30 mins troubleshooting why I failed emissions this last time, and answering my "theoretical" questions on how I could add some more power and still be legally registered. That said, they can be quite strict, he even checked when i first registered the truck that my fuel screw safety wire was intact.
Also go through a good importer. You can save a few bucks DIY but it's a minefield you don't want to wade into unless you really like paperwork. Also there's a lot of pitfalls and gotchas to vknow about the JDM auctions if you source one from there.
Don't be too scared of RHD. It slightly lessens the value of your rig, but it took me about a day to get used to, and now I enjoy the crazy looks people give me. I've seen literal double takes, and one woman even covered one eye with her hand to make sure she wasn't hallucinating
. Imo, the biggest downside to RHD is listening to the same "wHaT aRe YoU, a mAiLmAn? Hahahahq" joke from inquisitive idiots at gas stations.
That's all I can think of off the top of my head, I'll update if anything else comes to mind.
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