Help identifying possible dual pot light plug
Thos MR16 GU5.3 light bulbs are 12 volt bulbs. The GU10 bulbs are 120 volt. There is little to zero chance that this is some sort of &quot;Dual Socket&quot;. And if it were, it would still likely be just a 12 volt supply.
The round things in the picture are rivets that hold the fixture together.
To brighten the fixture, I'd recommend a bright, new LED bulb. Your fixture likely has a power supply with a watt limit somewhere, if you can access it, check the largest total watts you can draw on that switch and get a bulb as close to that as possible. If you don't know the power supply rating, then just try the highest output MR16 bulb you can find anyway. They usually don't take much power. Many of the fixtures were designed for incandescent anyway.
You might already have what WAS a bright LED bulb in that socket. Over time, and this is especially true of the early models made years ago, LED bulbs go dim. They may never burn out, but they loose brightness so an easy way to fix a dim fixture is to just get a new bulb. Looks like 75 watt equivalents are available. This one is rated for 700 lumens and consumes 9 watts but you might want to look for one that is Energy Star listed as they won't go dim as quickly.