JaneN
Sorry for the late post, saw your thread soon after you posted but I've only just logged in today.
Firstly please don't waste your money on the light you linked to, unknown trash that will probably die soon after purchase.
You'd be better off sticking with a reputable brand, I've used my Petzl Tikka XP headlamp with Eneloops for many years for running and all outdoor activities and still going strong. Mine is an older 80 lumen model but newer ones are about 350 lumens. IPX4 so no worries in heavy rain, used mine all the time in rain.
They are also very affordable, for you and for running I'd recommend the Petzl ACTIK Core which is USB rechargeable but can also take 3AAA batteries, or the ACTIK model (non-USB rechable) and power it by Eneloops recharable AAA batteries which will last you for many many years.
Great video here:
https://vimeo.com/206098790
Another good thing about Petzl is that they sell replacement headstraps, most other companies don't. Note I'm still on my original one though, and still in great condition as I store mine in a Petzl case, which is also worth buying if you plan to travel with it, again most other companies don't sell cases.
Lastly if you are serious about running and want to increase your performance, read about Scott Jurek the greatest long distance ultramarathon runner and how why he recommends a vegan diet.
https://www.huffpost.com/entry/ultramarathon-running-diet_b_1587874
Good luck with your training.