...interesting so for this latest version of the battery they are saying if the current draw is less that 0.05A or 50mA it shuts down in 50 seconds.
This is curious as the earlier version had a shutdown after 20 minutes.
The Bushmaster I believe draws between 40mA and 60mA. So at 50mA it is borderline whether the auto shutdown happens.
You may just have to try it and see - in the worst case you will just need to buy a grain of wheat bulb and wire in circuit.