My variety family fun pack arrived last night and they are good match for what I need, though one panel I have loose the 8mm are a match and another the 8.5mm. The button tops that come with are tiny, smallest size that will go over the plunger I guess, but look useful in the situation where you have a button missing...
Several ways you can go with that.. basically you'd be using those buttons as the attachment for a fabricated button, if it's a round one you could "turn" it from a piece of plastic or close grained wood to right profile and then slice the back off flat and glue or socket one of those little buttons on it. If it's a weird shape but you've got another one still sitting on the reset switch or something, you can do the old trick where you press the one you've got into modelling clay to make a face mould and then you can fill that with resin, let it set, or if you are really careful and make a jig to hold it in place, cast with one of these little buttons in place, otherwise, clean up the cast part and glue it on the back after. Also you may find a matching profile on another object, end of a marker pen, some bottle cap, and you can cut that down and glue on. Maybe also if you are "half good at 3D modelling for 3D printing" you could get something more or less the right shape and wouldn't have to do 200 prints to get the plunger fitting right.
Unicorn herding operations are proceeding, but all the totes of hens teeth and barrels of rocking horse poop give them plenty of hiding spots.