I was wrong in my previous POST. In the IBM 5160, grounding the DATA line, not the CLOCK line, is a method of getting the POST to go into MANUFACTURING TEST mode.
I brought out a known-good 5150 motherboard of type 16KB-64KB, one fitted with the final BIOS revision, revision 10/27/82. Keyboard attached. No 301 error. Booted to BASIC where my keystrokes registered on-screen. Powered off. I then removed the keyboard then I grounded the DATA line and then I powered the motherboard on. No expected 301 error and then I soon heard a never-ending series of beeps. Looking at the source code for the 10/27/82 BIOS, the behaviour appears to match the MANUFACTURING TEST mode (skip keyboard test, skip ..., run the POST in a loop).
Out of curiosity, I grounded the CLOCK line instead of the DATA line, and I observed the same behaviour.
I put in the 04/24/81 revision BIOS. Grounding the DATA line, I saw the cursor appear, no 301 error, and then after a long minute of a flashing cursor, the never-ending series of beeps started.
But there is beeping, and the POST appears to be running in a continuous loop. And I realised that your, "No 301 error shown", was not conditional, i.e. maybe you do see a 301 if the keyboard is removed. So the MANUFACTURING TEST mode hypothesis is gone.