So though not specifically done for a Kayak - this fully applies and writing this because I couldn't find a nice good guide/shopping list for building my own LED lights. The list below is what I leveraged to build a set of running lights for my Porta-bote - and given that the materials are the same will probably be repeated for my kayak once my wallet recovers from other recent fishing upgrades
Total cost for 40" lights, waterproofing, mounting & hookups - $49 - and it scales rather well - i could have done almost 16 feet plus for a bit over $100. This is significantly cheaper than the pre-strung ones you can buy but the quality will all depend on your skill
Some "notes" prior to the shopping list
1) I decided to mount the lights rather than glue as this makes it easier to repair (when i post pics you'll see my mounting goes around a complex shape). Tape was tested... and is WAY to unreliable. I know many people will us 3M Marine 5200 Sealant and glue to place LED lights - if you go this route and are following a normal kayak hull - the tubing will let you remove lights for repair or replace w/o having to re-glue all over!
2) I used shorter lengths of lights because it fit what i needed - but given the low cost of doing more - do it!
3) I went with 5050 because cost per lumen it worked out better - also the 5050 should dissapate heat better so should last longer. Heat is (and probably always will be) the primary cause of LED's failing.
4) Buy extra - its all cheap and it gives you wiggle room if you screw up - especailly of the tubing, endcaps, and sealant
1) LED Light strip - 5050
(I went with connector because i'm lazy but they do have w/o). Make sure and take off the strip of double-sided tape on the back since you won't be using and it could off-gas when sealed.
a. Tubing - 10mm
- it is fairly good quality.
b. End Caps
- I cut my own holes to match my wiring & used lots of sealant
(can also use to seal any holes for wiring and or screw holes you make!)
4) Mounting - Silicone brackets
5) Misc Items
a. Connectors (perm)
c. Type 3 marine wiring 18 Guage
d. Waterproof connectors (for removable connections)
e. 12v plug/cigarette style (because that is what i use on my battery box)
I'll post some pictures when i can
Feel free to ask questions and I'll answer