This is my opinion based on all of the rigs I've seen and owned.
The bulb goes between the filter and the motor.
If your fuel line is not bundled with the wires and cables, the bulb can be in the motorwell. That does make it exposed to sunlight and fish hooks.
The arrow should point UP toward the motor for best performance of the bulb. That is important to know when positioning the bulb, whether inside or outside.
The bulb position is more important with old carbeurated 2 strokes. An arrow pointing down can cause repeated problems with holding a prime.
The injected 2 strokes and 4 strokes rarely need to be pumped unless the fuel line has been disconnected or the filter has been drained.
Whatever you do, make sure that the fuel line has enough slack for tilting the motor.
Storytime..
One day we we're out in the "new to us 265" and we ran the main tank dry. My brother turned the fuel valve to the other tank, opened the battery hatch, pulled out that damn cracked plastic tub, and reached down and pulled up the bulb and squeezed it (we later learned that we never need to squeeze the bulbs when changing tanks.)
He left the bulb up high where you could see it. We finished out the day and docked and raised the motors. The next time out I lowered the motors and got underway. One motor died in the channel. I looked at the bulb and it had snapped the barb off. Holy $hit!!! It was up high and nothing leaked. the two open ends were just sitting there
...raising the motor snapped it