Broadly speaking, looking at the Au-Ga phase diagram one gets:
(Now, this is based on a paper from 2011, a more recent 2017 paper is open access).
Several things to notice (or get from the paper):
The solubility of gold in solid gallium can be considered to be zero.
The solubility of gallium in gold is not zero, but is on the order of a few atomic percent.
Slightly above the melting point of gallium, the solubility of gold in the liquid is also very small.
There are multiple intermetallic phases across the diagram, 4 of which are stable at (and below) room temperature.
Formation of an amalgam can be ruled out.
So, it is a pretty normal binary phase diagram. Now the phase diagram does not provide kinetics information, so the time needed to actually form any intermetallic compounds (and if those formed near room temperature would even be the equilibrium phases) is not known.
Now, if we look at how gold leaf is used, there is no glue used - the leaf is place, smoothed and hammered into place, and it just sticks. So try just sticking it.