How can I (safely) test this "toy" machine?

[Rive]

The catch is that the gear shift is designed to mechanically push on the switch

Might be a bit more tweaking, but maybe you could just replace the whole assembly?

Ali apparently has some...

 

[Averagesupernova]

Ummm, aren't we forgetting something?

Oh one last thing, when you get it running please post a pic with you driving it?

You bet I will!

 

[jack action]

Yes, I have Googled them muchly.

The catch is that the gear shift is designed to mechanically push on the switch - switch and gear shift are affixed in a framework so they come together just right. I don't think there's a lot of margin for error, so it has to be virtually the exact switch.

(The switch button itself is flat, not concave - not curved or notched - and it is opaque red, not transparent. Too bad I can't just point to a Google pic to show you what I mean...)

Also, it's 2-position, temporary-on. Most of those are 3-position.I have yet to find anything similar online.

Does this help:

https://www.ereplacementparts.com/forward-reverse-switch-p-1482485.html​

There is also the official authorized Peg Perego retailers' list for parts & service in Canada.