To answer your question:
1) Pull the money out of your IRA, since you are older than 59 this basically means pay in cash from savings. Very standard mustachian advice: only buy a car you can pay for in cash. Do some research on the tax implications of increasing your income by pulling from an IRA. Taxes are likely not a major consideration as you are both on Medicare (no ACA subsidies) and the standard deduction (24K for married couples) is so high losing out on itemized deductions is unlikely. I am not familiar with income thresholds for when social security gets taxed, but there may be an argument for spreading the IRA withdrawals over a couple years. IRA withdrawal is also a better option as it lets you buy a used car from a private seller.
2) If you want to buy from a dealer always see what financing options they have. Sometimes your car is actually cheaper if you take a loan (e.g. 1K cashback for financing even if you pay the loan off immediately) sometimes they have 0% loans.
3) At/near retirement age, I would not consider home equity as a tool to help spend (or even invest) more money. Generally owning your house outright is the best hedge against a bad sequence of returns on your investments.
4) Last time we bought a car from a dealership their max on credit cards was very low, $500. If you buy from a dealer you may as well ask to do the max and get a few rewards, but don't count on getting a lot on a credit card.
Unrequested advice:
1) Make a temporary plan for having only one car, so you don't feel like it is an emergency if the truck breaks down. THis seems easy enough since you are both not working, just make sure you are doing things together or are staggerred enough that you can have one pick up and drop off the other if you have overlapping commitments.
- Even working quickly be prepared for the new car buying process to take at least 2 weeks. Ideally, be prepared to wait longer to find the right private party used car or to be able to see a few months of dealer incentives.
2) Since you generally get rid of cars due to age/rust rather than mileage consider a nearly new, high mileage vehicle for your next car. If you can get a 3 year old car with 100K miles for half or less than the original MSRP you will have a car that looks great the entire time you own it and maintenance should be minimal.
3) Body rust isn't that big of a deal or a sign of imminent death. It isn't pretty, but given your cars age and mileage I would expect them to last another 5+years. I have a sixteen your old car, it has been rusty for years. I have done standard maintenance (oil, breaks, tires, battery) the only extras it needed in the last 5 years were two break lines, one hose, two struts, and an AC clutch, all of which were pretty easy to diagnose at home (hey look that hose is cracked, hey my AC doesn't work and it sounds like there is loose change rolling around in the AC clutch) and parts were around $220.
4) Consider learning how to do more of your own maintenance and repairs, so an older car feels less prohibitively expensive. Even though you have a facepunch worthy SUV and full size truck, the great news is those give you a lot more room to work if you need to make a repair. The idea of fixing a car seemed very intimidating but between youtube and the fact that "fixing" cars really just means taking a bad part off and putting a new part on, it is pretty doable if you are prepared to cuss some and have the repair take 4 times longer than you thought.
5) Feel free to disregard 1-4 since it sounds like you are already FI and just trying to be responsible with money/investments. It is totally fine to have two cars because you want to and can afford it.