Connection tracking for LB-algorithm of Least-connections(member)

Where is the LTM tracking which server it sent the connections to - specifically for the purpose of the LB-algorithm?

Is it "show sys connections" or some other table?

F5 is actually tracking the connections that have not been terminated yet (either active or idle) between the F5 itself and the pool members. You can play with "show sys connections" to view those connections but I would rather use GUI statistics or "show ltm pool MY_POOL detail" to get the current open connections for each members.

By setting the timeout to "immediate", the entries in the "show sys connections" table would be gone so that can't work with the LTM's LB algorithm.

Yes, Least connections (member) would not be a good choice in that case as you are almost immediately removing the new entries from the connection table. For information, I said almost immediately because there is a scheduler that runs every X seconds (I can't recall the X) which clears every connection that is elligible for deletion.

F5 cannot track current connections between your servers and other systems in the network. I wonder if It is possible using a SNMP or WMI monitor.