Explaination:

“My wits are running out.”

“Wits” is plural so “are” is used instead of “is”

If “Wit” was used, it would be: “My wit is running out.” because Wit isn’t plural.

“My cleverness is running out.”

“Cleverness” is not a plural word so “Is” is used instead of “Are”

“My wits and cleverness are running out.”

“Are” is used because you’re giving more than one thing that’s running out.

“My wits or my cleverness is running out.”

“My cleverness or my wits are running out.”

In this case, the verb takes the number of the closer noun.

If it was merely the capacity of one’s mental acuity (aka cleverness), a gramatically singular subject, then “is” would be appropriate. The proximity of the verb “to be” with cleverness is, perhaps troubling to the tongue, but I assure you: it is correct.

because it is plural

wits + clever = 2 things

is – for singular

are – for 2 or more