It looks like the Gateway 2000 Colorbook machines all used a SystemSoft BIOS, a notoriously irritating BIOS to work with. Here are the beep codes for that type of BIOS, pulled from a NEC Versa laptop's manual:
Beep Codes
Beep Sequence
Description
Note:
S = Short beep
P = Pause
L = Long beep
S-S-S-P-S-S-L-P
DMA page register failure
S-S-S-P-S-L-S-P
Refresh failure
S-S-S-P-S-L-L-P
ROM checksum failure
S-S-S-P-L-S-S-P
CMOS RAM failure
S-S-S-P-L-S-L-P
DMA controller failure
S-S-S-P-L-L-L-P
interrupt controller failure
S-S-S-P-L-L-L-P
80C51SL (8042) keyboard controller failure
S-S-L-P-S-S-S-P
Video adapter failure
S-S-L-P-S-S-L-P
RAM failure (no message is displayed)
It doesn't seem like it's finishing its error code. On some other BIOSs, 2 beeps indicates bad RAM or a bag graphics card. If it's using a different BIOS, maybe it's trying to indicate that instead. I'd remove the RAM and see if the error changes as a start, personally.