+50 pounds (deadlift) = +0 Pounds (bodyweight)
You don't have to gain any weight to add 50 pounds to your deadlift. People do it all the time.
I went from a 5RM of 265 to a 2RM of 365 while essentially remaining 180 pounds--and I was trying to gain weight. (Rather poorly--I might've started at 175 or 178, and a couple days later I was 178 again.)
Novices, in particular, can easily add 100 pounds or more to their deadlift without increasing their bodyweight. They'd get stronger faster if they did, but if they're like you and have a need to keep their bodyweight low, they just progress a little slower and lose steam a little faster.
I am not sure why you care about your 8-10 rep max instead of some other rep range. I would bet that such a goal is actually among the most counterproductive if you are looking to improve your deadlift numbers without gaining mass.
The standard prescription is very few reps for strength, medium-few reps for power, more reps for mass gain, and obscene numbers of reps for endurance.
I would expect that you would want to stay on the ends of that spectrum and avoid the middle of it like the plague, if keeping a constant bodyweight is important. Speaking generally, instead of about the deadlift specifically, I'd do 1-3 reps for strength, maybe some lighter sets of 3 done fast to work power, and some much lighter sets done for 25 or more reps to train endurance. (I wouldn't do 25+ reps of deadlifts. Air squats or another bodyweight exercise would be a better choice.) I would avoid sets of 8-10, or even 5 to 20, as I would expect that they would be hypertrophic, so in order to avoid gaining weight, I'd have to be very hungry. That would be silly.
All of this relies, as you note, on neurological gains. But why would you want to avoid those? If it's a purely esoteric question, then I would say that we probably don't have the answer. Separating neurological gains from muscle mass gains is very difficult and has a number of confounding factors. If this is a practical question, then it very much matters what your current bodyweight and strength numbers are, how much training you've done, how much training you'll have time to put to this, and how much other training you'll be doing.
As an untrained deadlifter, you have a lot of untapped neuromuscular gains, so adding 100 pounds to your deadlift probably wouldn't require any added mass. You might also get some benefit from working high-rep air or Hindu squats, low-rep pistols (unweighted for a couple months, then using a dumbbell or kettlebell to add weight), as well as singles or doubles of heavy barbell squats. My faint understanding of rock climbing is that one occasionally finds themselves in a compressed, squatty position, so strength in that range of motion could be helpful.
Your focus on pull-ups is probably ideal for your sport. The bench pressing you do is also likely a great idea for avoiding imbalances between pulling and pushing in the shoulder girdle. I'm no expert, but I've been having a lot of success recently with straight-arm overhead work (Turkish get-ups, waiter's walks, dumbbell and kettlebell overhead presses, windmills) to strengthen the shoulder as well. It's possible that these could be of some specific use in rock climbing, for those situations where you need to brace yourself by pushing your hands against one rock and your back against another rock.