The pronoun *ipse* is not a third person pronoun.
It can be used with the first or second person just as well.
The closest English word I can think of is "-self" from which one can form "myself", "yourself", "himself", and others.

Reference to first or second (or third!) person can be left implicit.
You can say *ipse sentio* ("I myself feel"), no need to say *ego ipse sentio*.

It is possible to use it together with *ego* or *tu* as well, and that gives more emphasis.
It also proves unambiguously that the pronoun can go together with first and second persons.
For a couple of examples, you can check uses of [*ego ipse*](https://latin.packhum.org/search?q=ego+ipse+%5Bcic%5D) and [*tu ipse*](https://latin.packhum.org/search?q=tu+ipse+%5Bcic%5D) in Cicero.