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Your biggest consideration here isnt weight, it’s high winds. Even with trellis a strong wind will put a lot of strain on the fixing point.
Fixing vertically down into the bricks I’d want to go at least through the first into the second course but fixing robustly this way you’re ultimately putting the load on the mortar, which may or may not be up to it.
This sort of set up spreads the load better. Some hilltop folk might go all in and run 4 inch posts into the ground, but if it’s short, light trellis and you don’t live somewhere windy then batten twice the height of the trellis with a couple of fixings.
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After building a whole kitchen and hanging cabinets I avoid the harder plugs. I use long strong steel screws and enough rawl plugs to match the depth of the screw. And I make sure to clear the plaster on top of the brick. Whole rawl plug needs to be in the brick and hole needs to match rawl plug size. If it spins in the hole it isn't secure. Some people put slivers of wood in the hole around the rawl plug in these cases to stop it spinning.
For really heavy things I have used resin bolts which are good fun. You drill a hole as per instructions, fill with polymer resin and push your threaded rod into the hole. Wait until it cures and then bolt whatever you need to into it. Solid.
Look up frame fixings and YouTube from actual builders is a godsend.
I'm still undecided about exactly what method I'm going to use but whatever it is will involve screwing something into a brick wall. I had intended just to use some fischer nylon plugs and screws but I've seen mention of concrete screws as well. What are the plusses/minuses of those compared to plugs?
Main question probably being which is least likely to come out?