Looking at your photo, there are two or three things that can leak there:
1. The exhaust "Y" pipe. The two bolts in the photo that are close together, along with two more bolts above, hold the exhaust Y-pipe to the transom bracket. It is made of aluminum, and the bottom can corrode to the point it start leaking. This portion of the exhaust is filled with sea water when the engine is off. When the engine is running, it is filled with exhaust and water mixture exiting the engine.
If the leak is the "Y" pipe, the leak will slow way down when the engine is running, and will increase when it is not. It also is likely to have a little leakage even running on the cuffs, which you reported that you did not have. You have to pull the engine to do any repairs to the "y" pipe.
2. The transom bracket seal to the transom. This will leak the same with or without the engine running, and will not show any leakage while on the cuffs.
Any leakage between the transom bracket and the transom will show up at this location, even if the leakage is up higher. The two outer nuts in your photo, along with 4 more? up higher should all be tightened. As others have said, hopefully that will fix your problem. One one older boat, I loosened them all about 3 turns (obviously out of the water), then went outside the boat and pulled the outdrive away from the transom a 1/16" or so in order to force 3M 4200 into the gap, then went back in and tightened the nuts.
The problem is...there is usually only one reason these nuts would not be tight...that is the wood in the transom is softening up

Soft (aka rotting) wood can make this a recurring problem, until it gets bad enough that a transom rebuild is in order. But you might be able to get 5-10 more years before a transom rebuild has to be done, if you stay on top of the sealing and tightening. This is the kind of thing that a marine surveyor should check for during a purchase.
3. Leaking raw water inlet pipe or hose. (this is not your issue)
This pipe and hose connection at the top of the transom bracket, could still have it's leak run down to the bottom where your photo is. However, if your raw water pump is the style mounted at the front of the engine, then this area has suction (not pressure) while the engine is running, so there would be no leakage while engine is running.
_________________

"Knot Easy" 2000 Horizon 240 Volvo 5.7GS /SX
tow: 2017 Honda PILOT EXL-AWD
prev. boats:
'87 Chaparral 198CXL 4.3 OMC Cobra
'69 Jetstar 16ft Ski Boat, 115hp Yamaha
'68 Aluminum Jon Boat, 3hp Sears
'64 Water Wings