There's good empirical evidence that the portion of property taxes that falls on the unimproved value of the land (ie, the location's value minus the value of the building), is not passed on to the renter:

http://gameofrent.com/content/can-lvt-be-passed-on-to-tenant...

In general yes, but I think Prop 13 complicates matters, because it's not just a lower tax rate, but rather applies unequally to different properties based on their transaction history. (e.g. a property built or sold recently gets high taxes, while one that's been unchanged remains low)

So we can divide the rental market into high-tax and low-tax properties. The landlords of high-tax properties must incorporate the tax into the rent. Meanwhile, the landlords of low-tax properties can set their rents just as high, since they compete in the same market, and pocket the tax difference.

In contrast, a flat property tax reduction would increase the profit margins of all landlords equally, and any one of them could start undercutting the others and be undercut in return, which over time in an efficient market will tend to lower prices back to a similar margin before the tax reduction.

It's primarily an indirect effect. Landlords won't buy/build new houses if the expenses would be too high relative to the rent the market is willing to pay. That lowers the supply and raises the rents in the long term. However, if you have an existing property, there are no guarantees that you can find a tenant who is willing to pay enough to cover your interest, taxes, and other expenses.