Where is the starter relay located?

Got a 1997 Thunderbird 4.6. The starter was staying engaged. Changed the ignition switch because after testing, found that the wire to the solenoid had constant power even after you start the vehicle, and key is in just the on position. While in gear the starter was hitting the flywheel only in park, reverse and neutral, not drive. Replaced the starter do to starter drive damage. Still have constant power to the solenoid when key in "on" position after starting vehicle. Have been told there is a starter relay on the vehicle. Have torn the dash apart, looked under the hood, traced the wire down to the fire wall so far, still no relay. Now by the battery there is a connection that the wire runs to, that has two wires going in and one coming out to the solenoid. What is that as well? It's round and about one and a half inches long. Thank you for any assistance you can offer.