Help identify please: power or manual gearbox?

The OP will need to take a closer look. Later LA 360's had a recess in the balancer/damper ring as opposed to the cast-in counterweight that stuck out. That one may have a recess. (Enlarge the pic for a better look.) Checking the casting numbers on the side of the block is a sure-fire way to find the engine size.
Could be possible but my money is on the not being a 360 for several reasons but I agree the best way to determine is look at the drivers side of block