remote linux box, cell connection, how to check wifi connectivity

I'm thinking a bit theoretically here, my linux knowledge is rudimentary, could anyone give me some hints:

If I have a remote linux box, connected through cellular data, what would be the best way to SSH into the box, initiate a local wifi connection (without losing the cellular connection), and check the local wifi connection?

I'm looking for a way to check local wifi connectivity without relying on the router/gateway/network.

Any input would be greatly appreciated,
Thanks!