I have tried to research this online and get confused. Probably addressed in questions here somewhere but have not seen it. My dad is WWII vet now going to memory care. He did not have a pension as he was never designated disabled in any way. From what I understand you are given disabled labels of say 10%, 20%, etc. And that's fair, if he was not disabled he should not be designated as such. But still would like to get every assistance fairly available, if any. If he does not qualify for any benefits, then we know. I do know he could go to a VA contracted nursing home but most of them nearby are full. That said, is he eligible for any monetary or other benefits from the VA? Their income is low at this stage, but they do have some assets. From what I read in some places, his assets may disqualify him from any additional help, but in other places I read it may not.
I'd go straight to the VA; call them. Your father doesn't need to be disabled to get the basic medical care, which I believe is the first step. He would be assigned to a team, with a Social Worker. That SW is the individual who can provide guidance through the system as well as information on what's available to him.
You could also contact the American Legion or VFW, but you'll have to find out from them which branch handles basic medical care qualification to get started. Another option which is probably quicker is to determine if there are any county or state VA agencies that can help get him qualified for the basics. Then you go from there to find out what services specifically are available to him.
Good luck. Dealing with the VA is challenging, but I've found the workers at the VA Hospital to be very, very helpful and compassionate. It's partly a matter of "resetting" your way of thinking to be able to navigate the VA system, admittedly confusing.
This is from the Veterans benefits tab on this site.
Aid and Attendance and Homebound pension don't seem to rely on service disability. There also does not seem to be an asset limit.