Brooky Hi, I have a 2005 4 stroke 115 hp and am new to boating. My boat also did not give a warning horn at key up. I can't say about your boat but came to find out that my motor which was built by Yamaha in those years, doesn't have a key on alarm. Now if your boat had a key on alarm and now doesn't that is totally different.
Anyway. I did as you and tested the horn to make sure it worked grounding out the tan wire in the forward controls and it came on. To assure myself that it would work during a malfunction I was told to ground out the oil pressure sensor while running. My oil pressure sensor was on the port side top of motor best reached removing the plastic flywheel cover. All I had to do was pull the rubber boot back from the top of the oil sensor and touch a jumper wire from the top of the oil pressure sensor to the side of the same sesnor (or engine ground) and my horn sounded immediately. That gave me comfort that the system is working. The oil sensor on my boat is designed to "open" the contact above 22 lbs pressure so not supplying a ground. If the pressure drops below that the oil sensor "closes" the contact and establishes ground.
Hope this makes sense.
Cheers,