Perhaps a bad fan resistor
You don't, the dealer or repair shop does.
The repair manual for a 1962 Impala may be found at the internet site Chilton DIY under 1962 Chevrolet Impala Repair Manual Online. This manual will contain all the information needed to repair or service a 1962 Impala.
only one side will move forward
The purpose of this forum is to provide information on how to repair things and not to bypass them. The best thing you can do is repair the problem correctly.
The best thing to do is go to bgfindeashop.com and locate a repair shop that has the BG chemicals. They will install a cleaner then back flush the system including the heater . Then they add a fluid conditioner.
Haynes repair manual Chevrolet Impala SS, Caprice models 1991-1996 chapter 6
You need to take it to a repair shop that has the equipment to properly repair it.
Check with an older repair shop or go to the public library.
It is cheaper to replace it. Finding someone to repair it is almost impossible.
The method of repair depends on what is broken or worn the steering column. In a 1963 Impala has universal joints and couplings that can wear, as well as electrical connections. Any of these will wear over time.
Replacing a wiper motor on a 2004 Chevy Impala can be difficult. It is best to take it to an auto repair mechanic or an authorized Chevrolet dealership.
I am sorry but you don't and you will need one to clear codes after the repair.