I don't think there's usually need to have a separate ping timer: just have each client send the sequence number of the last received packet in their response,

I don't think there's usually need to have a separate ping timer: just have each client send the sequence number of the last received packet in their response, and the receiver can subtract what they think the game state should be at vs what they're really at to determine the difference in time every packet without having to only be able to sync up the time every ~2 seconds.