I agree with
@AussieHJCruza WD40 is not a penetrating oil. I'd be cautious using acetone, as it will dry out rubber, which may lead to future cracking. CRC, PB Blaster & Sea Foam are all have penetrating oils.
First I'm just trying to give you some basic mechanical advise. Your series 105 transfer case linage looks different than what I'm seeing in the 2000 100 series Land Cruiser FSM (factory service manual), so I'll be of limited help. You need some of the 105 guys to step-up to the plate and help out here. Possible the 80 series is more like what you have, check with that sections of mud as well.
Hopefully you examined old gear lube for amount, color, water (cream white gunk), metal pieces or any contaminate as this can be revealing. What did you from drained gear lube?
Note: It's necessary to replace gear lube drain & fill plug
washers (gaskets) when every removed, or they leak.
Looking at your pictures, I doubt the ball & socket of the linkage connecting arm pivot points (that was covered with the rubber boot) are frozen. It looks to me as if boots are doing their job. Easy to determine, just twist the linkage connecting arm back and froth slightly clockwise then counter clockwise. It will not twist much, but if it twist any, even tightly (new would be tight), it is not frozen. Actually it does not look like any of your linkage is frozen to me.
Ripping off that boot, you'll need to replace it once shifting problem solved. Check with a local Toyota parts department, you may need to buy linkage connecting arm to get that boot. You can cover with marine grease as a short term fix, but not yet.
Keep driving until transfer case gets too normal operating temp. Stop, put in neutral and try shifting transfer case to low. Make sure you follower your 105 owners manual shifting procedure precisely. Keep repeating once or twice a day, over next few weeks (exercising). And keep adding your penetrating oil of choices to linkage nuts, this is to make removal of nuts easier. The more you do both the better your chance of freeing this up without pulling T-case, and easier time you'll have removing linkage connecting arm nuts.
While doing above detriment if shift handle lever is frozen. This should be apparent now just by moving shift handle back and forth. If it rocks a little, moving linkage a little as it does, then shift lever is probably ok. After the two week procedure, if no change in condition, then remove the nut "A" to free up shifter handle lever from linkage. Now try moving shifting handle lever. If it moved freely full distance, that's not your issue.
Next would be to see if you can move shift arm "C". But this will impossible to do, and since other above points you've checked are working properly, I'll bet this will not move. Even in a loose transfer case, this takes a lot of muscle to move even when using leverage of shifting handle lever & linkage. It's not likely (looking at your picture) it's frozen externally. So bottom line if exercising T-case doesn't fix issue, you'd need disassemble top end of transfer case next. I don't not recommend you do this on your own. First you need correct FSM & tools along with good mechanical skills. You'll need hands on help for this.
I'm still very hopefully your transfer case has just frozen up. If you're not hearing any weird sounds from it the gears, there're probable ok. If you get any improvement over next few weeks it will be a very positive sign. There may even be other chemical's you could add into transfer case, too help loosen up first and better lubricate second.
Good luck.
