Last year I purchased lights for my Strida. I was looking for ones that would remain on the bike when folded and which would be powefull enough to be very visible in the traffic.
The interesting features of this light systems are the following:
They are as small as a watch.
They are superlight and weigh only 17 g each!
They have an integrated Li-ion battery that can be charged on the USB connection of a PC. The charge takes 1 hour max. The front light has a 5 hour runtime in flash mode. The rear one has a 12 hours runtime in flash mode.
They are really bright. Although they are primarily meant to be seen, in a complete dark environment it will provide sufficient light to see the road 5 meters in front of the bike, which is enough up to a speed of 15…20 kph.
I use both lights in flash mode and I can see the reflection of my front light on traffic signs located at least 100m ahead!
The front light is easy to fix on the steer with the supplied velcro strap. The rear one is ideally fixed on a seat bag with the clip. Before I had the seat bag, I used an L-shaped aluminium strip as holder. That strip was fixed on the plastic seat support.
Note that the new Blackburn Flea model now has a charge indicator which mine didn’t have. It sometimes happen that I end my trip to the office with a weak light. but nothing would prevent me to recharge the battery at regular intervals, I’m just too lazy to do so…
After one year, they still work very well. I did not use them during the summer, but that did not affect the battery life.
Please, please do not use the flash mode. The idea is that you get more attention and that works, yes. But it is dangerous for people around you and yourself. A brilliant blinking light is a hazard to look at. It is a heavy distraction for other cyclists and drivers. Their eyes can not adjust to it.
The other reason is the calculation of the distance. With a flashing rear light you can not recognize how far it is away. Try it. You can not recognize if the distance is increasing or decreasing. Here is just not enough time see if it gets brighter/bigger.
I use the B+M Toplight Line. This is a rear light with an integrated reflector. Like the original Strida rear light, it fits on the carrier. It uses a standard AA battery. The front light is an B+M Ixon IQ, which contains four standard AA batteries. The front light has two modes - 40 lux and 10 lux. 10 lux is enough to ride in a completely dark park. None of the lights has a flash mode.
Tom, I somehow agree with you: in a totally dark environment, a flashing light is not appropriate.
I use my Strida on lit cycling lanes so car drivers do see my silhouette when they see my lights…
The front light can be seen from far but is not a hazard to look at compared to some other much more powerful lights. In Belgium, people immediately identify a flashing light with a cyclist, which is not the case with steady lights.
On my very low recumbent bike that I sometimes use on dark roads without cycling lane, I have an Ixon IQ at the front and a Blackburn Mars 4.0 at the rear. The last is the German version and has no flashing mode . But it is maybe better so . In addition, I have Reelights SL 120 attached to the wheel hubs. They don’t have batteries but are powered by magnets attached to the spokes. They provide constant good visibility and are not too brilliant.
May I introduce my solution to a near invisible taillight (invisible at daytime, at nighttime it will show up alright!!)- works with the Brooks B67 , maybe other saddles can also cope…
Misuse your Strida-tool, adapt a LED-light and hide under the saddle!
. But it is maybe better so 
. In addition, I have Reelights SL 120 attached to the wheel hubs. They don’t have batteries but are powered by magnets attached to the spokes. They provide constant good visibility and are not too brilliant.