You asked for rudimentary info, so I hope this helps...
You could use a 12V 7Ah rechargable lead acid battery, the type used in emergency lighting and alarm boxes. They are easy and cheap enough to come across.
For the 5Volt part, you could buy an off the shelf DC to DC convertor such as
https://www.powerstream.com/dc6.htm. I have no affiliation with that site and have never purchased from them, link included just to show what you may be looking for.
You can wire directly to the 12V battery for the controller, use a suitable inline fuse.
Use the DC convertor connected to the 12V battery, again with a suitable fuse. And on the 5V side of the DC convertor to power your leds, Again put an inline fuse on your leds. Never hurts to be cautious.
That I believe is the simpilest solution. The leds should draw less current on flashing mode. If they are only on half the time they should only use half the current over time.
With the above setup, you should be able to squeeze it into a small enough enclosure under the saddle or attached to the cross bar. You may even be able to design the enclosure and make it a feature of the bike!
The above setup should last a few hours. If you need a longer operating time you could put a second battery in parallel. If you have a different 12V source you can use that, the setup would still be the same.
The DC to Dc convertor is switched mode, this is more efficient then trying to knock up a linear convertor for yourself.
I hope this helps.
Edit* While I was typing the above, I see the original poster found what he was looking for. Just like me to be late to the party
Next time!