I noticed in the 15.0 IOS documentation for the Catalyst 2960 switches the 'test cable-diagnostics' command is present and it indicated it works on both GigabitEthernet and FastEthernet ports. That made me wonder if 1) it really does work on the FastEthernet ports and 2) if it tests all four pairs. I suspected it would not given how Fast Ethernet doesn't use all four pairs but I thought I would test it. Here is what I saw:

Switch#test cable-diagnostics tdr interface fastEthernet 0/1
Link state may be affected during TDR test
TDR test started on interface Fa0/1
A TDR test can take a few seconds to run on an interface
Use 'show cable-diagnostics tdr' to read the TDR results.
Switch#
Switch#show cable-diagnostics tdr interface fa0/1
TDR test last run on: March 01 00:03:19

Interface Speed Local pair Pair length        Remote pair Pair status
--------- ----- ---------- ------------------ ----------- --------------------
Fa0/1     100M  Pair A     0    +/- 15 meters Pair A      Normal
                Pair B     0    +/- 15 meters Pair B      Normal
                Pair C     N/A                Pair C      Not Supported
                Pair D     N/A                Pair D      Not Supported
Switch#

Pretty much what I expected. Now if I could find a cheap 2960c model with Gigabit Ethernet....