Wait. I’ve been and looked up what the Tamiya paint is. Enamel in a mini tin for ants is what I used to use as a kid. This spray on stuff appears to be a lacquer rather than an enamel or acrylic.
Is that going to hold up well being softer?
I was going to use black epoxy and a clear epoxy gloss over it. One badge I need to get white lettering into it to reverse how it is now. I will need black, then some white and sand off the white (to leave the recessed bit white) and gloss clear over it.
Stick the badge down onto some wood with double sided carpet tape.