I've seen other riders with pulsing lights during the daytime, sun or no sun, they are extremely effective at letting drivers you are there. Remember I clearly stated at the beginning of this thread it's about being seen and a strong concentrated pulsating (far less annoying than the flashing ones) LED will do that in the brightest of sunshine. If you are worried about battery life then there are plenty of Lithium options or just use AA rechargeables.
Squeaker gave a very good
suggestion but not sure I'd mount it on my helmet but it would be excellent attached on the bike and I believe they now go up to 150 lumens. I've now got
this on my helmet and it is an excellent light (designed for runners) and will do for now. I managed to get it for £10 but I've noticed the seller has doubled the price. For the time being I've given up the search for a helmet mounted pulsating LED light with 180 deg visibility that can be angled at will say for map reading. The Cateye came close but once it's on it's fixed. Think I was looking for too much.