Well if you want to try hopper shaking maybe you have one of these, or could get one:
My firewood hauling pickup truck needed down in the meadow the tires air pressures increased to 50PSI. So instead of hauling down an inverter-generator and one of the air compressors I used coupons discounts to buy this. Will be needed safety equipment anyhow for the moving van with six, 65 PSI truck tires and no spare wheel and tire.
The better of these have a vibration held up singing away to open air pumping.
Then if it works could be operated by one of MattR’s recommended electronic timers and an automotive relay.
AC powered voltage try one of those old Oster hand band massagers gotten used:
Perhaps a bit old topic but I wanted to add some ideas.
Depending the type of fuel being used, someone can consider adding some weight inside the hopper, on top of the fuel. This will be pushing downwards the fuel.This is useful for low density material.