I'm sorry he is not himself and understand your concern.
Given his age, it could be that there is an underlying medical issue.
While the other cat in the neighborhood could certainly be factor, I'd want him checked over to ensure we are not missing anything.
As he is skittish, unsettled, more vocal and possibly hungrier, I would be keen to ensure his thyroid hormone levels is normal (a simple blood test) and he does not have blood pressure.
I'd also consider a urine analysis. I suggest this rather than a stool analysis as his stool is solid. Oftentimes, the accident is because the cat feels like straining due to a bladder issue (such as cystitis) and stool passes.
At this age, a high percentage of cats start to get arthritis and initial signs can be subtle but we do sometimes see stool outside of the tray. Due to this, I'd ask the vet to thoroughly check his joints, especially his back and hind limbs.
After his check up, we will hopefully have a clearer idea of what is going on.
At home, keep a close eye for any other signs and ensure he has the ability to come inside whenever he needs to (with e.g. an open cat flap).
He should always have access to 2 clean litter trays.
Do also keep track of his eating and drinking habits to ensure they are not changing.