Since it makes the noise while under power, I would tend to assuming that it is related to the forces on the motor. When driving forward, the force of the thrust is pushing the motor .
So I would see if I could make the noise happen by putting downward force on the lower unit while trimming. You can do that in two ways; either with the motor off and someone standing on the lower unit with the motor tilted halfway up ( and not running) or with the motor down, running and the boat well tied off at a dock. The second method would probably more closely simulate the conditions that you hear the noise.
Although it may not help at all, I would check the tilt fluid level and top off as well as grease any zerk fitting .
The comment about relay noise may also be a clue if there is a bad relay it may be snapping in and out under current load. In that case, if the clicks are far enough apart, you should be able to see if the movement of the lower unit also hesitates.