Max distance for 2x8 pergola rafter span
I would think you'd be safe at 13'. Although it's not an exact comparison, 13' seems to be "in the ballpark" considering there won't be much load on them.

Here's what I'm basing my opinion on:

Max. Live Load 20 lbs/ft2 (956 N/m2)


https://www.engineeringtoolbox.com/horizontal-roof-rafter-span-d_1484.html

And also using this calculator to try various wood species and spans, etc:

https://www.awc.org/codes-standards/calculators-software/spancalc

I think how the "rafters" are attached might have some significance for you too.