If you’re experiencing issues with the GPU on your 27-inch iMac A1312, there are a few potential solutions you can try:

1. Reset the PRAM and SMC: Resetting the PRAM (parameter random access memory) and SMC (system management controller) on your iMac can sometimes resolve issues with the GPU. To reset the PRAM, restart your iMac and hold down the Command + Option + P + R keys until you hear the startup sound twice. To reset the SMC, follow the steps outlined in Apple’s support article.
2. Check for software updates: Make sure your iMac is running the latest version of MacOS X. Software updates can sometimes include bug fixes that resolve issues with the GPU.
3. Disconnect peripherals: If you’re experiencing issues with the GPU after connecting a new peripheral, try disconnecting it and see if the problem persists.
4. Reinstall MacOS X: If you’ve tried the previous steps and are still experiencing issues with the GPU, try reinstalling MacOS X. This can resolve any software issues that may be affecting the GPU.
5. Contact Apple Support: If the above steps do not resolve the issue, it may be a hardware problem that requires repair. You can contact Apple Support for assistance.

If the GPU issue on your 27-inch iMac A1312 is related to a hardware problem, it may require repair or replacement of the GPU. This can often be done at an Apple-authorized service center or by Apple support. It’s best to contact Apple Support for further assistance in determining the issue and the best course of action.