Gravity doesn't work well enough in a small boat bouncing around at sea. I was a tad confused by the picture of the improvised sextant.
Measuring the angle between sun/star/planet and the horizon is much more consistent than using gravity. A sextant allows for ship movement while allowing an accurate elevation angle.
I don't think any measure of gravity (local vertical) was required.
The way that type of signal mirror sight works[1] is that you align the reflected light beam from the sun with the line between the hole in the mirror and the hole in the sight.
My guess is that he did that, with the horizon as the target, then recorded the mirror tilt angle, and doubled it to get the sun to horizon angle.