It's possible.
Toyota offered OEM-style Turbo timers (actually manufactured by someone else, but looks OEM), I've never seen one that fits the MKIII before, mainly because the MKIII has unique switch sizes.
Toyota has some standard cutout sizes that they like to use, I know of a Turbo Timer for sale right now that fits into one of those (it would fit perfectly in my AE86 if it was turbo, haha), it was originally sold as an accessory for the SW20 MR2 in Japan, and it has 3 switch positions, 1 MIN, 3 MIN, and off (which is the center position, without 1 or 3 selected).
Looks pretty nice. They may have offered one for the MKIII at some point.