I found the connection but I don't know the cause:

Running test_imaplib prior to either test_datetime or test_tarfile causes the latter test to fail.  test_datetime seems to fix the problem for test_tarfile if it precedes it.

[1/3] test_imaplib
[2/3] test_datetime
test test_datetime failed -- multiple errors occurred; run in verbose mode for details
[3/3/1] test_tarfile
2 tests OK.
1 test failed:
    test_datetime


[1/3] test_imaplib
[2/3] test_tarfile
test test_tarfile failed -- Traceback (most recent call last):
  File "/mnt/9707/edelsohn/src/cpython/Lib/test/test_tarfile.py", line 1953, in test_list_command_verbose
    self.assertEqual(out, expected)
AssertionError: b'?rw[39 chars]-01-05 18:19:43 ustar/conttype \n?rw-r--r-- ta[6470 chars]f \n' != b'?rw[39 chars]-01-06 00:19:43 ustar/conttype \n?rw-r--r-- ta[6470 chars]f \n'

[3/3/1] test_datetime
test test_datetime failed -- multiple errors occurred; run in verbose mode for details
1 test OK.
2 tests failed:
    test_datetime test_tarfile