I forgot, if you are selling this to a dealer he will have a notary, most businesses do, I am a notary and did it all the time for my business. Title transfer require notary and get a notary friend or ask the person if this private sale to get one.
Finally, keep forgetting stuff. Okay so most states do not require notarization, but some do, regardless it is the best way to cover your butt. Proof that you are no longer responsible for the car in case new owner does not register the car. Most auto clubs, AAA for instance will do this title transfer, paperwork and notarization for a small fee of nothing. You can also both people go to the DMV and do it there.
Take him to MVD to have them notarize the signature of the sale of a car. I owned an automobile document service company in the 1970s and MVD is quite particular about signatures and witnesses. Check with your MVD.
It's dangerous or at best inefficient to make stuff up -- I see people giving their opinion on this site, of things that are not a matter of opinion. Sometimes law and medicine aren't as black and white as we might wish, but for something like this, you're looking for facts. So when there's an expert around like Heiser, take advantage. Or, for example, if you're concerned about the particular rules of your state, I promise you that the answer to your question is on your state's DMV website -- and that it won't tell you you have to drag your arthritis-ridden Dad physically to a notary or the DMV. Put the extra energy that trip would cost you, into getting a PoA for your dad, so you can continue to help with whatever comes up in the future.
I got a POA as soon as my folks began to not understand what things they should say yes to. Thankfully, they were willing because they needed assurance that someone was looking out for them. I wondered if they would hesitate over the item about taking care of selling property, even R.E.. I said to them "only if you need me to help with reading the paperwork and helping you understand what they are asking". As it turned out he died first, she was suffering from dementia, and we needed to get her out from under a house payment she couldn't afford after she lost most of their income. I signed everything until the closing and felt she was able to do it and it would help her remember that she participated in the sale. (had a wonderful compassionate R.E. agent who helped me with good advice).
Indeed if your father is willing, get him to give you a durable power of attorney, to facilitate such transactions in the future. You'll need the notary just one time, when you sign the POA, but thereafter just your signature will suffice to take care of business for your father.
A notary can come to your dad's house. But, whatever his signature looks like would be OK, anyway. My MIL had a stroke on her dominate side and her signature is entirely different. (I have a friend with no hands. I should ask him what he does about a signature.) This conversation reminds of all of the schools that aren't teaching script anymore. :)
With all due respect to Mr. Heiser, DMV of each state have their own regulations and rules about the transfer of automobiles, and I too have a POA for my husband, but could not revoke his driver's license with the State of AZ. They want me to physically bring him to DMV to have his signature notarized by them and to identify himself. Food for thought...
My POA worked except for getting info about my step dads medical bills. It isn't any help after they die, evidently. Wanted Mom to go to lawyer and get paper saying she is executor of his estate. I told them, no! We only wanted to know if they sued the hospitals for doing tests and transporting him to a second hospital to have the same tests and he was clinically dead already. They got him breathing on a machine, and thought it gave them the go ahead to run up charges. I got copies of the bills (because I take care of my Moms bills). They were paid NOTHING! (serves them right)
One last comment from the peanut gallery, a notary only attests to the person's identity, that is why the person shows the notary their identification, whether the signature is a mark or indecipherable is not at issue, the id is what is important.
Everyone tells you to get POA on dad....you have to have him sign that too! But that, if done properly, will help into the future if dad gets worse, or if his mental capacity diminishes. If he becomes demented, you will be stuck unless you go for guardianship. Get notarized to play it safe....