No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
Should be just fine, if you want to go for additional FICO style points as you're paying that car note ahead, see what it does to your payment date... if it pushes it out into the future by a non-trivial amount (not all lenders will do this but most will if you're overpaying on regular payments), pay it nearly down to $0 but not off ($20 balance or whatever is fine), and then let it sit at that level for as long as possible unless the LO tells you to pay it off for DTI reasons which will be unlikely.
Optimization for EX FICO 2, handy to have an almost paid off installment line on your report... and highly useful for FICO 8/9 too.
Beyond that just sit on your hands credit wise, or if you need to do anything else do it like right now, and other than optimizing your revolving utilization before you make the mortgage application you should be golden.
BOFA like most big banks I've read about is hit or miss currently in terms of mortgages, but that can change in 2 years so I'd simply suggest not being tied to an individual lender right now and look closer to when you're ready to pull the trigger.