I should have looked up your p/n before posting. Anyway no harm done. The part is generally referred to as a link but it is part of the clutch rod arrangement.
These are some of the tractor models that have that part in case you have to do a salvage yard hunt.
G10748 LINK Case parts 600B-SERIES, 630, 430CK, 470, 300B-SERIES, 320, 430, 400B-SERIES, 320B, 420B, 420BD, 530, 530CK, 300-SERIES, 500B-SERIES, 570 LINK
Your tractor is one of the models in the 300B series, 310B is a utility tractor that only built in 1958 & 1959. If the model/serial tag still exist post the serial nr so we know which year it was built as some parts change by serial nr. If the tag is missing post a pic of the steering wheel and I will be know the build year.
Don't assume that the part is 5/16", I will check in the AM and post back if it is other than 5/16".
The link is the Caseih parts catalog for 300B series tractors.