A young man in his 20’s believes to be the actual ghost of Jim Morrison, using the body as vessel, he sets forth on a journey into the heart of the desert where he believes to find a ‘Gateway to Heaven’.

For your consideration:

Believing himself to be the reincarnation of Jim Morrison, a young man ventures into the desert in search of the ?Gateway to Heaven?. (23 words instead of 41)

For your consideration:

Believing himself to be the reincarnation of Jim Morrison, a young man ventures into the desert in search of the ?Gateway to Heaven?. (23 words instead of 41)

Because you only have about 25-30 words to work with you should cut where possible.

"he sets forth on a journey into the heart of the desert"
"Journey's to the heart of the desert."

Don't say someone sets forth, or starts, or begins. In movies characters don't "begin to walk", "they Walk." They don't "set forth on a journey," they "Journey."

"A singer who believes he's possessed by Jim Morrison, journey's to the heart of the desert to find a 'Gateway to Heaven'"

The problem is you have no conflict. What's standing in the protagonists way? You should at least hint at what's opposing your lead characters goal in the logline.

Hope this helps, good luck with this!