Note that local garage as an avoid at all costs POI on your satnav, you've already proved by driving it normally since that its an intermittent fault only
It doesn't sound like a gearbox fault at all, its possibly an electrical or contact or simple adjustment problem in the operating solenoids.
I would try another Toyota garage first as they will be familiar with these, try and find a smaller one, possibly in a more rural area where keeping existing customers might be regarded as more important than in a chain urban site.
If not a good old fashioned car sparky might be able to find the problem switch, if not he should be able to by pass the problem and give a direct to starter circuit...not saying this should be considered a permanent cure but the car needs a bit of old fashioned diagnosing by elimination, not by throwing new parts at it method till we happen upon a fix.
Autobox specialists are a minefield, i would only suggest using one that comes via personal recommendation.
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