I've been practising/trying to manual and wheelie for a while now (with a fairly solid focus – rather than just slacking off and cruising on easy quiet bits of my ride) and whilst nowhere near consistent, it is fully the weight shift that is needed, not "pulling up" per se; it's pretty similar to the weight shift you use to get the front wheel over a log or up a step, but sort of over emphasised.
I found that it came on heaps after concentrating getting my front wheel cleanly up a curb or similar for a while – it gets the unweighting of the front wheel to become a comfortable feeling. Then take that and push the envelope more (and fall of the back a bunch!) until you find the balance point.
Maintaining the balance point is the hard bit and seems to be just practise, practise, practise. Which I've not done enough of yet!!!
Make sure you are in an easy gear too; being able to have that accelaration to drive the feet under the hips towards the bars helps ridiculously for both manuals (half to one revolution of the cranks then balance) and wheelies (continually pedalling)
However, from that I'm starting to be able to bunny hop better now too, although I'm sure I "cheat" a bunch with SPDs
***And for the spelling pedants 😆 it is practise with an 's' – the US version is with 'c'