Did the mechanic start the car by jumping the twoe starter solenoid lugs?
If it started right up with that then your problem is in the start switch circuit
The +12VDC lead from the battery goes to a Terminal near the ECU (3 red wires)
then a pair of red wires to the ignition switch Lugs #30
from lug #50 at the ignition sw a pink wire to the start switch connector

The pink wire at the connector goes to the Common of the shifter switch
The swiched lead of that switch is a BLue wire back to that start sw connector
Then there's a Blue/Green to a connector at Left A post
then another connecter at the left suspension tower then
finally a Blue Green to the Starter solenoid.
You have to have +12VDC show up at the small starter solenoid lug to
engage the starter. It should be easy to attach a test lead to the solenoid
to see whats happening with your voltmeter.

My book shows a single pink wire breaking out of the harness by the coolant overflow bottle this is to start the car from inside the engine compartment
by applying 12v directly to the shifter interlock sw.
This would only bypass the ignition sw and the 12v terminal by the ECU

You certainly need new mechanics, as they have just replaced stuff
without diagnosis from what you say.

You can look at the inhibitor switch and see if you lose +12V
at either the Pink or the Blue/Green wire to narrow down where the fault is.
Can be a bad connector, a ratty crimp lug, but it sure is a PITA when
the fault is intermittant. When it quits you can try tugging on the blue green wire from the starter back to the shift switch. But do the voltmeter thing to
narrow down where you're losing the +12V

Do you have a good schematic?

Bill