Affixing Wood Strip to Headliner

[Plangstraat]

I would like to affix a thin strip of wood (1 inch to 1/2 inches wide by approximately 7 feet long) to the edge of a curved headliner on my Nordic Tug 32 to cover up some small holes. I have attached a photo of the headliner area.
I don't want to drill into the fiberglass behind the headliner and am wondering if anyone has used adhesive to affix wood to a smooth vinyl headliner. The strip of wood would be thin, bendable and lightweight.
The interior is teak but I was thinking of using a less oily wood to ensure that the adhesive would "stick" to the wood.
Any suggestions or words or wisdom from anyone who has tackled such a project would be much appreciated.

 

[Max1]

ShoeGoo.

Its clear, Super strong, sticks to almost anything, flexible and cures quickly.

It's my go-to flexible adhesive, other than the usual boating adhesive for exterior waterproofing.

 

[Pascall]

Degrease the teak wood with acetone, then you can glue it perfectly!

Gtoet,

Pascal.