I asked the guys at Ignitech
https://ignitech.cz/en/ which of their offerings would be a good one for the Savage, and this is the one they recommended:
https://ignitech.cz/en/vyrobky/tcip/tcip.htm.
I ordered one and it is on my desk right now:
The price is very reasonable, 175USD, so if it functions there is no longer any reason to hunt for the original Igniter anymore, unless if you are a purist who wants to keep everything original. (if this description fits your profile, shoot me a PM, I have one for sale

)
The staff is easy to communicate with and they take pride in delivering a plug and play solution, which they did.
It plugs right into the harness with the right connector and the bike starts up as it should and it runs like it did with the original ignition module.
As you see, apart from the connector to the harness, it also has a cable protuding with a serial interface connector. this is used to progran the unit.
If you want to purchase one of these modules, be sure to have a way to connect your pc to it, with either a pure serial interface, or the USB to serial. In the latter case you will need a PL2303 Prolific driver installed.
This driver is notoriously tricky, and in my case, I could not get it to work on my trusty WIN7 machine, but on the WIN11 laptop it worked well.