Usually devices of this type aren't EEPROM, they're usually either mask ROM or OTPROM. If you're lucky the world has changed, and it is indeed flash/E^2.
The existence of programming/JTAG pins is a good sign though - it's a sign that it's not a mask ROM. There isn't hardly anything you could do with a mask ROM as far as a hack. If it's OTPROM, there are a few hacks. First of all, if you're really clever, you can overwrite existing data. OTPROM/EPROM works by electrically breaking links. This is where the term "burning" comes from - a link is physically was blown or burned. In later iterations of the technology, the EPROM, this is actually done with a charge on silicon in the burning process. It's reversible with ionization from UV light. You always start with a field of one state and change to the other with a programming voltage, and reverse the process/clean the slate with the UV. You can always open more links - changing zeros to ones. This is where the hack comes in - with the right bit masking, you might get lucky an be able to make a change w/o erasing the chip. I've actually done this in the field once. Luckily, our engineer found a single line of code (in 8051 assembly language) to be changed, and the bitmasking allowed me to program over the existing ROM w/o erasing. In this case, we were using cheap PROMs instead of EPROMs, and IIRC i dind't have a blank, so this saved me an extra road trip to Des Moines. :-)
The other hack you can do is very hardware. OTPROMs are typically EPROMs w/o a quartz window. You might be able to physically remove the blob over the die. This is a common hack. You can chemically remove the epoxy w/o damaging the silicon die, and from there continue with your hardware hacks. (Probing, re-routing, or _erasing the EPROM._ xD) When you do this, be sure to shield the die, lest room light will cause erratic operation.
Have phun!
-P