Did a little bit of testing with mine this morning. The only way I can get the tap tempo to work is with an FS-6 setup as per the manual, then connected to the SY-1 via the centre output jack on the FS-6 with a TRS cable. The 'A' footswitch on the FS-6 then gives tap tempo.
I tried an FS-5 in all combinations with no success. I don't have an FS-7 to test, but suspect it'd work in the same way as the FS-6. (TRS output using a TRS cable.)