On my '85 & '89 Supras, quick blinking CE light meant no codes stored. I wouldn't sweat it.

My neigbor had a Celica that was failing emissions for high HC, and the fix ended up being a new thermostat, his was stuck partially open, and never allowed the engine to warm up properly. If yours has never been changed, do it, and use OEM parts, maybe a new thermostat/gasket and radiator cap.

I think the thermostat may be a PIA to change on the runner, it's actually in the front middle of the engine instead of on top, like most I've seen, this according to a toy mechanic.