I can't read the codes my OBD1 Chevy is throwing. I install my jumper, turn the key and the light comes on, blinks once really fast and stays on. I tried disconnecting the batteries and the computers fuses but to no avail, the light stays on and the computer refuses to blink off the codes. Anyone heard of this problem?

Are u sure you jump the correct pins?

I had the same problem with mine , it turned out the previous owner had tampered the SES light and hot wired it to the alternator/battery light. Had to remove the instrument panel and re do the wiring , everything works now. Check if the A pin (top right) is correctly grounded.
You can also connect a small light directly to the PCM SES light output and trigger diagnostics to se if there is any problem with the wires to the SES light.
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I can't read the codes my OBD1 Chevy is throwing. I install my jumper, turn the key and the light comes on, blinks once really fast and stays on.

What is the problem you are troubleshooting? If you are troubleshooting a "no start" condition, and you cannot read the computer codes, that usually means the computer itself is fried... I had that problem on a Ford F-150.

I'm jumping the correct pins, I've done this plenty of times before.
The light does work.
The truck starts and runs, it simply won't read back the codes.

Is it on now? if it is not, the bulb may be burnt?

yes the bulb is on, while driving and trying to read codes.

I took a look through several service manuals and tech manuals to see if there was anything that would or could cause the bulb being on thingy.... In a Haynes Tech Manual I ran across this info.
Within a section regarding general DTC info it talks about normal operations i.e., 10 seconds to set codes after a problem etc. the next item says that there is an exception when a code 53 is set. (Code 53 is not even in the GM Service Manual Set) However, it says that it will lock the CEL (SES) light on until Power is removed (It says ignition is turned off, however Ignition will not remove codes, Battery Power has to be removed to clear codes. *shrug* try Removing both Batteries power for a few minutes and see if it resets the ECM and Clears the Constant light On Problem.

I realize you said you removed battery power in your original post, however, I would let it sit for awhile WO power to see if it will allow complete ECM reset. If not sounds like a short in the ECM wiring harness.

I'll try again, this time I'll leave the batteries disconnected for the majority of the day. Hopefully that will do something. If not I'll look into that DTC# 53 that you mentioned.