Q: Macbook Pro 2012 does not accept SSDs

any SATA enabled logic board on a MacBook Pro made after 2007 should accept an SSD (I suppose ANY logic board with SATA connecters are eligible for an SSD in reality)

You may have damaged something with the board or if you are using any 3rd party software with the SSD is could be incompatible.

Do the drives work in other computers or is there no option to test this?

The symptoms you have described indicate that the odds are the internal SATA needs to be replaced.  Do so and the SSDs should be recognized when installed in the MBP.

Ciao.

The SATA cable is very fragile and when damaged can function when a slow drive (read mechanical HHD) is installed but not when a fast drive (read SSD) is. Replace the SATA cable and your SSD should be usable again.

I have the same MBP with the Samsung Evo 850-series 500gb. SSD and it works just fine.

your post reads like you may have to reset SMC, NVRAM, PRAM

Sometimes on boot up a Macbook will be looking for the original hard-drive however it can not find it.

A reset SMC, NVRAM, PRAM may fix this problem.

Also remember to reset SMC,PRAM, and NVRAM on your MBP

http://www.macworld.com/article/2881177/how-to-reset-your-macs-nvram-pram-and-sm c.html

How to reset NVRAM (or PRAM)

If your Mac is not booting correctly or one of the functions listed in the previous section is acting strangely, you can perform a simple reset of your Macís NVRAM or PRAM. Resetting your Macís NVRAM or PRAM will reset the data stored to its default setting. (Note: As always, we strongly recommend having a complete backup of your important data before troubleshooting your Mac.)

The process for resetting PRAM and NVRAM is exactly the same. Simply follow these steps:

1) Turn your Mac off.

2) Turn on your Mac and when you hear the startup chime, immediately press and hold the Command-Option-P-R keys. (Note: You may need a wired keyboard for the reset).

3) Hold the keys until the Mac restarts and you hear the startup chime for a second time and then let go of the keys.

After resetting NVRAM or PRAM you may need to reconfigure some of your Macís settings. If you are still having issues with your Mac, you might want to consider resetting its SMC.

What is SMC?

On Intel-based Macs, SMC stands for System Management Controller. The SMC chip controls your Macís sleep function, power, various lights and indicators, fan speed, and keyboard backlights among other things. So if your Macís fan is out of whack, indicator lights are misbehaving, it wonít respond properly when closing the lid, or the Mac wonít turn on at all, you might want to reset the SMC. (Note: Again, be sure to have a complete backup of your important data before resetting the SMC)

How to reset SMC in a MacBook with a non-removable battery

1) Shut down the Mac.

2) Connect your power adapter to your Mac and to a power source.

3) With the Mac powered off, press Shift-Control-Option and press the power button at the same time.

4) Release all keys and turn on your Mac.

Good. 

Ciao.