I tested on a debug router but it isn’t really a viable solution.
There are messages logged but they all have topic route,debug,calc and there is no specific message about the recursive route that goes up/down, only information about the reachability of a specific address occurring somewhere in a check-gateway, like:
Resolved link IP/8.8.8.8/30-25/2 via 8.8.8.8->IP/192.168.200.1/20-10/2 FLD{1} rr tr has metric BEST/32