Keeping wiring neat

Hey everyone, first time poster here.

I recently bought some supplies to run some of those adhesive LED light strips and am ready to give it a go. My plan is to install them on the inside lid of my storage/passenger box and pass the wiring directly underneath to the battery. I’ve got some male/female terminals so I can remove the box without having to undo any wiring. I haven’t decided yet whether I’ll hook up an in-line fuse directly to the battery or if I’ll tap into the accessory power line which is already on a 10a fuse (my winch is also tapped into this line so it’s only hot when the ignition is on). Suggestions are appreciated here. The lights are rated for 12v but I have no idea how many watts they actually put out yet.

Ideally, I’d like to run all the wiring and install the toggle switch so that I can keep everything hidden and weather proof in the hollow of the moulded plastic in the box. My concern here is that there’s no easy way for me to get to that area without cutting away some of the plastic. I’m OK with doing that, but I have no idea how I’d reattach things and keep it looking neat. Caulking is about all I’ve been able to come up with and I imagine it’ll be clumsy at best.

I’d appreciate any advice and/or product/material suggestions. I’ll attach some photos in a few minutes to help illustrate what it is I’m trying to do exactly.