Thank you for your answer!Not too hard if you can solder (or want to learn) and are handy with your hands.
A quick google for "dub siren circuit" turned up what looked like some sensible results.
Maybe find a circuit you're interested in and post it here to see if people think it looks legitimate.
These people are even selling kits, which are often a good way to get started in electronics:
Got this answer from seller:In that case trace out the connections going to the pitch switch and make a list of the resistors going to it.
Most likely they will be in decades, probably the 220k, 22k and 2k2.