Nice wee bike that… Servicing shouldn’t be an issue tbh, your troubleshooting sounds spot on so I bet 10 pence it’s either the switch assembly itself or some misalignment stopping it from engaging. So not affected by servicing. And should be a cheap fix too, unless it’s a loom fault.
If it was me, I’d bridge out the switch (assuming it’s a normally-open, which it probably is) and see if that fixes it, to confirm. Then work from there- check the stand’s actuating the switch well, to see if it’s the switch or how the bike’s working with it. But tbh this is just because I’d want to walk into the shop and say “here’s exactly what’s wrong”. You don’t really need to, it’s just information is power.And you’re about 10 minutes from confirming your diagnosis, or disproving it, anyway.
I wouldn’t permanently bypass it though!