Electrical

Which idiot lights are flashing?

i had dashboard idiot lights flashing in my old hilux, the trailer plug was wet and full of mud,do not know if this could help you bye barry

If all the lights are flashing I would be looking at the ignition switch as it switches ALL to ON at startup to check they all work. If it is contacting then not, the check system will go into spazms. Could be a loose connector under the steering column doing the same thing.

Earthing wires on eyelets bolted to chassis or cab metal also could be loose.

Had this happen to a 80 series the problem was where the alternator plugged into the main loom,needed to be cleaned.

In the 100 it would be alternator but the 105 doesn't have the computer smarts of the 100 so might be different.
Did you check the alternator output fuse?
Have you used a multimeter to see if the battery volts go up when you start the truck? That would prove the alternator is charging?

Lcool.org is the best resource for landcruiser problems.

All interesting comments as I've been having a similar problem with my 1992 HB30 Coaster (4WD). In my case the "T Belt", "Battery" and the "Filter" lights all start flashing or simply stay on for different time periods.
I've checked all the items and there's nothing wrong and as it's been going on for some years now, I've just ignored the lights.
I've always suspected a loose connection or a wire earthing out somewhere so I might check some of the above suggestions.

Mate
I have the same model and it was water getting in thru the windscreen on the
left hand side. water was dropping onto the computer which is under the glove box even set off the horn in the middle of the night, have seen it now on a couple of cruisers Fixed the windscreen problem went away
Cheers