In touch with him. En rapport; in sympathy. The allusion is to the touchstone, which shows by its colour what metal has touched it.
To keep touch—faith, fidelity. The allusion is to “touching” gold and other metals on a touchstone to prove them. Shakespeare speaks of “friends of noble touch” (proof).
And trust me on my truth, If thou keep touch with me, My dearest friend, as my own heart, Thou shall right welcome be.
George Barnwell (1730).