Can I use the word "resonance" to describe the connection between two people?

There are many senses of resonance - the pre-eminent ones connected in some way to sound and other metaphorical ones.

OED sense 2. is the one that concerns us here:

2. Corresponding or sympathetic response; an instance of this. In later use also: the power or quality of evoking or suggesting images, memories, and emotions; an allusion, connotation, or overtone.

One of the examples (the most recent one) given is:

2001 A. Solomon Noonday Demon (2002) ii. 77 Bill Stein's story has had considerable resonance for me.

You therefore have strong grounds for using resonance in the way you suggest.

Though resonance can be used here, it's less common than saying you resonate with a person. It's an unusual usage that will probably stick out to people.

You might find "affinity" more appropriate as it's used in its noun form to mean an innate connection with a person.

affinity

1. a natural liking for or attraction to a person, thing, idea, etc.
2. a person, thing, idea, etc., for which such a natural liking or attraction is felt.
3. inherent likeness or agreement; close resemblance or connection.

Source: Dictionary.com

I prefer wavelength as I feel it is more appropriate when describing rapport between people (or the lack of it)

(idiom) on the same wavelength, in sympathy or rapport

[Dictionary.com]

Usage:

There are older guys out there who can be great mentors, but you might not be on the same wavelength because of the age gap.

Harmony might be a good choice for what you are trying to express. In that case since you are inverting the meaning you could also use dissonance.

...There are older guys out there who can be great mentors, but you might experience a lack of harmony because of the age gap.

or

...There are older guys out there who can be great mentors, but you might experience some dissonance because of the age gap.