There's a couple of things to be (very) wary of:
The outputs from the FPGA are not guaranteed to be able to drive TTL levels, so some kind of level shifter might be needed, which would also serve to protect the FPGA board. That's assuming your monitor is expecting TTL levels. Do you know the input level specifications?
Ice40Beeb defaults to VGA, and it's possible that the 31.25KHz VGA would cause damage to the monitor. I would look to disable the VGA mode to be safe.
Honestly, I would say an old LCD TV with a SCART input would be a safer bet. But it really depends on your level of competence here.
In both cases, the pins to use are:
R = PMOD 9/10 pin 5
G = PMOD 7/8 pin 5
B = PMOD 9/10 pin 6
Sync = PMOD 7/8 pin 12
(Pin numbers are BlackIce pin numbers, see diagram above)
The 1MHz bus is already present internally in the FPGA, so bringing the signals out to the PMOD connectors would be possible. But again, the levels are not TTL levels, so some kind of level shifter would be required to be electrically compatible with original devices.
What device were you hoping to hook up?