How to teach a toddler to spit! Seriously…

I have received really great advice in the past here. I know this is probably one of the dumbest questions asked here today, but unfortunately, my son will need to test for COVID in the coming month. The lab doing the test prefers to do the saliva test for kids but my son isn’t even 3 yet(will be in about 3 weeks). He barely even spits when brushing teeth. He does the motion, but doesn’t actually have anything come out. Sooo, how do I teach him to spit so much saliva to be able to do this test? I don’t care what kind of advice or ideas there are. Everything will be considered.

The alternative is the nasal and throat swab. It can be done and of course he will just have to if he can’t learn to spit. We are not in US and unfortunately the medical industry isn’t as good at training bedside manner with patients where we are right now. Honestly they are a lot rougher than they need to be. Either way, any thoughts on how to get my toddler to learn how to spit will be greatly appreciated.