@Steve Neul
GORILLA HEAVY DUTY CONSTRUCTION ADHESIVE in past used to be used for building headers with at one point time. a lot of jurisdictions no longer allow it to be used as it does not have proved proper bonding surface.
since it does not spree out like wood glue.
Some jurisdictions do not require any glue be used due to the plywood is just a spacer to get the proper width as not a structural area. If the header is being made up of a series of laminates there's all kinds of codes of how the glues are to be applied and how they're pressed {clamped} together a whole different topic.
if Your jurisdiction doesn't require glue most likely has a nail pattern that should be used.
I looked at South Park construction drawings for headers they are slightly different from one drawing to another because of Architects but there is a pattern the width over the space you're trying to bridge the number of nails required per square foot. there is a lot to it.
A lot of the construction styles 20 plus years ago no longer meet a lot of the jurisdiction requirements for building codes.
example
like a roof sheet of approved of material
asuch, the nailing schedule is typically the familiar 6 inches on center at supported panel edges, including gable-end walls and 12 inches on center over intermediate panel supports.
Check with your architect or your building codes Department to see if they require glue and if so what is their recommendation they usually have a type not a brand that is required and most of the ones that we still do use are waterproof glues it only take a couple hours to set up and then can be totally soaked.