A better alternative for "second next"

Solution 1:

"The next page but one". This is certainly idiomatic and would be understood.

Solution 2:

"The page after next" works.

Printed examples that refer to something two pages later:

In the sidebar on the page after next, Bill Pearson, longtime comics writer, artist, and editor, reminisces about Reed Crandall and his art.

The first model output in the page after next has as the input Halo Active GRPs and prompted advertisement recall of Halo Active.

A more detailed analysis of service retirement benefits begun this year is given on the page after next.

Solution 3:

"Next but one"? Perhaps it might be an option local to the UK, or maybe even more regional than that, but it's certainly a phrase I'd naturally use. So for your example:

He suggested to me to read the next but one page