Vanishing elements of prime power order

An element x in a finite group G is said to be vanishing if some (complex) irreducible character of G takes the value 0 at x. In this article, we prove that every non-abelian finite simple group, except SL2(4) and SL2(8), contains a vanishing element of prime power order whose conjugacy class size is divisible by three distinct primes. We use this result to obtain the following generalization of a result of Robati (2021): If G is a non-solvable finite group in which the conjugacy class size of all the vanishing elements of prime power order has at most two distinct prime divisors, then G/Sol(G) is a direct product of copies of either SL2(4) or SL2(8) where Sol(G) is the largest normal solvable subgroup of G.