Noting the brackets are decoration only and have no purpose in the structure at all. If not, what are the alternatives.
Selleys No More Gaps is not suitable for this application due to the product being highly flexible and won’t cure hard.
The best product for this is Selleys Plasti-Bond Heavy Duty Bog, as it has an excellent adhesion to a variety of surfaces inside and outside the home. It is a two-part bog filler that can be sanded, drilled, and screwed into once cured.
For best adhesion to the timber you are filling, ensure the surface is clean, dry, unpainted, and free from grease or oil.