Essentially each wallet would have a static (or dynamic) "PON address" that would be hashed with the ip + block to provide key: (ip address + pon address + relayed block = key) That hash would then be added to each relayed block. A certain amount of blocks later, let's say 120, as long as full node was still active, they could redeem a set value.
It depends on what you mean by "check if still active", I can write less than 100 lines of code and using about 50 MB of memory and virtually no CPU usage and 0 storage, I can run a fake node that is capable of appearing "active" by accepting incoming connections, relaying the block(s) I want to receive the incentive for.
All it takes is an open socket, keeping a couple of hundreds of headers (<50 kB) and a handful of blocks (<40MB) in memory, not relaying transactions, not verifying anything, not storing anything on disk either.