As I mentioned in the previous post, the Time machine continues to back up stuff even when there seems to have been very little activity on the machine (it acts as server on 10.5, it has a lot of reading accesses to get learning material, videos etc.).
But how can I find out what the TM is doing? It looks like newer versions of the OS do have tools for monitoring TM, but my old 10.5 does not.
I found two tools that should be helpful – TimeTracker and tms, but none of them worked for me (TimeTracker crashes).