I think that you must use the
According to the Cambridge Dictionary
used to refer to things or people when only one exists at any one time
We have got only one sun shining in the sky.
the light and heat that come from the sun
Butterflies fluttered about in the sunshine.
The house, with its fresh coat of paint, looked lovely in the sunshine.
In the village square, people were milling about in the sunshine.
But take into account what @FumbleFingers has mentioned:
Sunshine (along with sunlight and daylight) are normally seen as "omnidirectional" (the light comes from the whole sky, not just the sun)
Google Books has no written instances of his back to the sunshine, whereas it claims About 141,000 results for what I consider the natural version: his back to the sun
Maybe you should rephrase it using the sun instead of the sunshine.