I am totally confused. The following formula that you say works is simply looking itself up on the same worksheet.
=VLOOKUP('TEST DAY 1'! A12,'TEST DAY 1'!A12:N14,13,FALSE)
It is not looking up anything that matches one worksheet to the other worksheet. You could have entered the following formula in B97 because that is all the Vlookup formula is doing.
='TEST DAY 1'! M12
In the worksheet that you uploaded, the row labels appear to be different to the row labels in your original screen shot.
It appears to me because of the different layouts of the worksheets, all you really need to do where you require a value from another sheet is to type an = sign in the destination cell and then change worksheets to the one containing the required value and click on the source cell and then press Enter.
PS. This has been added with editing my post:
Some of my confusion is due to the following.
In your Screen shots in your last post you have B97 in "Test Day 1" and M12 in "Month 1 Week 1".
In your example workbook B97 is in Month 1 (Week 1) and M12 in "Test Day 1".
I still stand by my comment that you can populate Month 1 (Week 1) B97 with the formula ='TEST DAY 1'!M12