If you like that Cygolite well enough, try some heavy duty Velcro or 3M hook and loop tape. These come with very secure tape adhesive and plastic hook and loop closures (not fabric). I use this for my Ion Speed Pro video camera helmet mount. I back it up with nylon zip ties but so far the adhesive alone has secured the camera mount shoe to the helmet. And the video camera is much heavier than that Cygolite. Aiming the camera isn't critical because of the ultra-wide angle, near-fisheye lens.

The tricky bit is mounting it where you want the beam. Most bike headlights are very directional and need to be aimed fairly carefully (which too many cyclists neglect on the local MUP - they blast their lasers straight ahead into everyone's eyes).

That's why the Light & Motion Vis 360+ is so well designed, with an adjustable headlight. But it's expensive.

If you just want an affordable to-be-seen helmet light and will rely on a bike mounted headlight as your primary, I'd recommend the variations of the Vivo-Bike Illuminati. I've used one for more than a year. Highly recommended as a to-be-seen light.

It's not currently available on Amazon from Vivo-Bike, but I see apparently identical lights from other vendors. They all look like this:



This vendor has 'em for about $12.

This vendor for $20, with free same day delivery for Prime subscribers.

These specs provided by Vivo-Bike all appear to be consistent with my experience:
Runtime: High=3 hrs, Med=5 hrs, Flash=12 hrs (might be slightly shorter now after a year of frequent use)
Charge time: approx 3 hrs, depending on charger
Weight: 50g
Length 66, Width 29, Height 22mm

Pros:

• It's very lightweight. You won't notice the weight.
• The strap is stretchy and secure enough for a road type helmet with vents, without crushing or damaging the foam padding or shell. Never popped off, even when I've crashed.
• The light is very directional, and intensifies wherever you look. It gets drivers' attention in traffic. When I see cars quickly approaching the street from parking lot driveways or about to roll through stop signs I look directly at them. The perception of a flashlight being aimed at them gets their attention and they stop.
• Very good side visibility due to the lens design. Much better side visibility than my Serfas and Light & Motion lights.
• Easy to operate on the helmet without looking at it. One big button cycles through high, low, flash and off. In daylight I check the reflection in my handlebar or mirror. Usually I want it on flash in daytime and traffic.
• The 300 lumen maximum output seems accurate. It's as bright as or a little brighter than my Serfas SL-255 on high and flash.
• It's weatherproof. No problems in several rainy rides.

Cons:
It's really a to-be-seen light. The beam pattern is mediocre, so it's usable only as a supplemental to-see light. It illuminates where I look, which is useful on the trails and unlighted rural areas. But the beam pool is splotchy and uneven due to the design of the reflective mirror that concentrates the beam to be directional. It sort of mimics the Busch & Muller lights reflective mirror design, but not very well. So don't rely on it as your primary to-see headlight.