Hello... You should be able to add log entries for router manger by adding the following to the default log filter...
"RtMgr" "RtMgr.BFD" "RtMgr.Client" "RtMgr.HAL" "RtMgr.If"
"RtMgr.Kern" "RtMgr.Server" "RtMgr.Table"
"RtMgr.VLAN"
To add log entries based on the above, run the command - "configure log filter default add event - This will add entries based on changes that are made to the respective event. I don't have a switch in front of me but I would guess that the "RtMgr.Table" log would add entries based on routes added or removed. You can add all of them as well and get log entries for all of the RtMgr events, just do that command with each one.
Give it a shot and let me know...