You'd probably have better timekeeping from a reasonably connected Pi with a common NTP daemon (take your pick, some are easier to configure / query), and a realtime-ish thread to emit your PPS signal on a GPIO or similar.

Probably more robust than line of sight, and able to pool with other NTP servers in your home-lab (and beyond).

True, but I'm not thinking of a practical method, just fun. I already have GPS derived time here, but that's been reliable and boring!