I think "No More Gaps" is you best option here.

It is quite flexible so can be used if you think there is going to be a bit if movement.

https://www.selleys.co.nz/products/our-brands/selleys-no-more-gaps/overview/

+1 for Selley's No More Gaps.

It remains flexible when cured, so will move with the gap over time.

Yip, a flexible caulking product like No More gaps is perfect for this 

I think "No more gaps weatherboard" is even more flexible than the standard product. Do a bit of reading to check before you trust that though.

timmmay:

 

I think "No more gaps weatherboard" is even more flexible than the standard product. Do a bit of reading to check before you trust that though.

 

maybe instead of saying "i think", you should check its correct first before posting?

This is hollow. 10mm wide. 

https://www.bunnings.co.nz/pinetrim-12-x-12-x-2-7m-untreated-finger-jointed-kiln-dried-pine-quad_p0307401 and stain to match timber,

or https://www.bunnings.co.nz/pinetrim-plus-18mm-x-5-4m-white-plus-quad_p0043747 and paint to match wall.

Attach to the side that stays put only, so the other side can slip underneath when it moves.

As gbwelly has posted, a bit of timber.

Quad or Quarter round as I prefer to call it as posted above. Or

Even something like some glass beading may also work and look a little different https://www.bunnings.co.nz/pinetrim-18-x-11mm-2-4m-h3-2-clear-pine-glazing-bead_p0293439

or even just a bit of plain square https://www.bunnings.co.nz/pinetrim-18-x-18mm-x-2-4m-h3-1-d4s-clear-pine_p0293022

wellygary:

 

Yip, a flexible caulking product like No More gaps is perfect for this 

 

 

In that vid he caulks it then runs a finger along then wipes up the excess. I've always found that makes a poor job and much prefer to mask first against the wall with a few mm to the gap, then caulk, then wipe the finger (or use a tool) then pull the tape for a perfect finish.

There's another problem that I discovered. The wall isn't plumb. It'll look awkward to put a trim along as I checked. 

I'm thinking if Sikaflex MS bond is better, too. A bit pricey than Selly's. I've never used it. 

Jase2985:

 

maybe instead of saying "i think", you should check its correct first before posting?

 

What, you want useful, referenced information, rather than vague memories? That's not the GZ way?!

Checking the product pages (standard, exterior):

• Standard: 300% elongation/stretch and up to +/- 20% movement capability
• Exterior: 500% elongation/stretch and up to +/- 25% joint movement capability

Not being an expert, I guess movement is more important than stretch in most cases, so there's a small advantage to the exterior version.

And for completeness.  Sikaflex MS has +/- 25% movement capability

https://nzl.sika.com/content/dam/dms/nz01/b/sikaflex_ms.pdf

chez:

I'm thinking if Sikaflex MS bond is better, too. A bit pricey than Selly's. I've never used it.