You're right about the rovergauge not working on a 14CU, forgot about that. A switch from a 14CU to a 14CUX is quite easy though, plug and play. I put a 14CUX from a '92 in my '89.If the OP is in the US as would be indicated by the flag next to his registration, the '89 has the 14CU EFI system, not the 14CUX. The difference being the ability to read codes among other minor things. I don't know if the Rovergauge will work on a 14CU system. I do seem to recall, years ago, people were using 14CUX EFI ECU's in these 14CU trucks and wiring up the connector to the code reader. You'd have to do some research and of course locate a good 14CUX EFI ECU to be able to do this (along with a code reader and harness) but that's one way to do it.
The 14CU and 14CUX computers used whats called EPROM, or Erasable Programmable Read Only Memory (in this case, the fuel map). This type of chip does not have any non-volatile memory, meaning that all recorded data (like EFI codes) are stored in volatile memory and are erased when power is removed. If the light is coming back immediately, (I assume you mean the instant it starts, not within 10-20 seconds or so, that could be something different) this is may be due to an internal memory checksum error, which, due to the nature of how these computers are fabricated, is not realistically repairable. While not a dirt cheap solution, I would suggest purchasing a newer 14CUX computer (plenty on ebay) and interchanging it. The 1989 does not have the harness for the small LED code reader box that came with later rovers, but it does have the 5 pin diagnostic harness (under the seat next to the computer, white connector with 3 wires and one loopback plug). The corresponding USB FDTI to serial cable is available (link below) and can be used with the rovergauge software (available for windows on github). Switching out the computer and using the rovergauge diagnostic software will give you the error codes (all of them, if there is more than one). I had a pesky EFI light on my '89, did the above, and found the code was being thrown by the park/neutral safety switch not responding (talk about an obscure thing), which I never would have figured out otherwise. My 2 cents.Bummer I cant add it.
I have an EFI light that just wont go out.
Even if I remove the battery and hold the red and black together to power it down.
EFI light comes on immediately
Then I'd try swapping the computer from your 90 into the 89 and see if the light come on right away. If so, it's something other than the computer itself, and will require a diagnostic like rovergauge mentioned above.I do have a computer and a code reader from my old 1990. Not sure if that helps.
I just went and unplugged the computer and plugged it back in and the EFI light still comes on immediately when starting.
Not sure if it matters, but the light is dimmer than the rest on my dash when it is running.