I have had a Bisun lamp for 12 or 14 years and have been very pleased with it.
I have not caved this year and when I charged and ran it yesterday it dimmed after only an hour, with the battery voltage right down.
The battery pack is 3 * 1.2V NIMH and the charger came with it.
I have made up a set of 4 * 1.2V NIMH of lower capacity (2800mAh).
I believe the charger and lamp will accommodate the higher voltage.
I am monitoring the charging current at 770mA, but every 5 seconds the current drops to a lower value then recovers. It seems much too regular to be a fault.
After a bit of thought I decided that this must be tied in with the charger's ability to decide when the pack is fully charged, but Google doesn't come up with anything.
Is this right, or have I done something silly?

https://batteryuniversity.com/learn/article/charging_nickel_metal_hydride

It may be the higher voltage is confusing the charger.

You are both right.  The pulsing is due to control software in the charger unit.

When the battery is on charge its apparent voltage becomes higher than when it is off charge.  So "the higher voltage is confusing the charger", absolutely right but the charger is aware that it is being confused by the battery's apparent voltage.

The charger therefore turns off the charging for a few seconds to let the battery "relax", and then it measures the battery voltage while it is in the "relaxed" state and off charge.

If the "relaxed voltage" shows that the battery needs more charge then it delivers another charging pulse to the battery, and so on.  This is all OK and perfectly normal.

You may find the pulse rate and pulse length (the so-called mark-step ratio) also varies according to the level of charge in the battery, in other words the charger gets bolder at certain times and whacks the energy in, and at other time it gets more cautious and delivers tiddly bits of energy.