How to modify a head-light to glow brighter using a dc to dc booster. The aim was to enclose all components into the lights existing case.
After completion, it was tested against a previously made 'booster' which had used the circuitry from a garden light. A similar design can be seen at:
https://www.instructables.com/Headtouch-Booster/

The third head-light had no modifications.

Supplies

Dc-dc booster module
Switch
Connection wire
Head-light

Step 1: The Voltage Increasing Unit

The voltage from the battery is increased using a module found on line at:
https://www.ebay.com/itm/mini-dc-dc-Converter-0-8-5V-to-DC-5V-Step-UP-Boost-Module-for-Breadboard-Arduino-/271734570473
It increases the voltage to 5 volts output.

Step 2: Fix Into Head-light

Fix the dc-dc booster module into the head-light. Solder a wire from the light to Vo (output), connect a wire from the battery negative to the middle connector, connect a wire to Vi which will connect to a switch and on to the battery positive. Connect a wire to the battery positive which will also connect to a switch.

Step 3: Add a Switch

Fix in a switch and connect to the previously installed wires. Glue in place. Close the cover. There wasn't much spare space to do this.

Step 4: Add in a Resistor

It was observed that a resistor was required to limit the current to LED. I chose a 120 ohm one.

Step 5: Testing

The completed head-light was tested against 2 other head-lights for brightness and voltage measured over time.
They were:
'normal' = with no modifications.
'boost' = with a voltage increaser from a garden light. The one shown in this link is similar but lacks a switch :
https://www.instructables.com/Headtouch-Booster/
'super charger = as described in this instructable. Later, a 120 ohm resistor was added to control current input to the LED. It shines less bright than before as can be seen in the photo on the right. But it is expected it's batteries will last longer.
Measurements were made ever hour, recorded and then graphed.

Step 6: Takeaways

The 'super charger' described in this instructable made the head touch glow very brightly for a hour or so, but it caused the batteries to heat up. This is likely why the batteries didn't last very long compared to 'booster' or 'normal' head-lights.
The 'booster' gave good brightness with a slight decline in voltage over time. There was no heating up of the batteries.
The 'supercharger' was able to run on batteries which wouldn't light the other 2 head-lights. It was very good at sucking out any remaining energy from a 'flat' (less than 1volt remaining) battery.

Step 7: Results

1. Brightness:
'supercharged' started out very bright but diminsed over a couple of hours. A case of 'Burning twice as bright and lasting half as long'.
'Boost' started bright and remained so for about 8 hours, then dimmed considerably.
'Normal' wasn't very bright but didn't diminish much for over 12 hours, A case of 'slow and steady'. Both 'Boost' and 'Normal' were still glowing after 40 hrs. Even after 8 days and nights (192 hours) they were still just glowing - as shown in photo above. Surprisingly, the light from them was still useful.p>

Step 8: 18 Days & Nights Later

'Boost' and 'Normal were left on. After a couple of days and nights they were only glowing dimmly but could be used somewhat for limited illumination.

After 18 days and nights 'Normal' had stopped working. 'Boost' was still glowing dimmly and did provide enough light to dimmly make out objects at about 40 cm away. Better than no light at all.

As can be seen the batteries had changed colour due to the zinc casing becoming delapatated. They were removed from the head-lights to prevent the corrosive of terminals.

Conclusion:
1. They both glowed for over 2weeks, much longer than expected for zinc-carbon dry cells.
2. The 'boost' modification, improved brightness and duration (Though, as it was also a more recent head-light. There is a slight possibility it was also more efficient.)
3. If dry cells are left in appliances and deteriorate, they are likely to 'weep' and corrode terminals. Hence why is is recommended to remove batteries when the appliance is not used for an extended period of time.