LEDs not lighting up with reverse bulbs on my truck
Sounds like they either "burnt out", or you have a break in the wire, close to the supply.
According to specification on the sellers website, for over voltage burnout you would need to exceed 14.8V.

Which for a truck, actually is not unlikely.
Many trucks run parts at 24V with 2 batteries, but I'll assume you haven't made that mistake.

Lead Acid batteries have particularly variable output voltage depending on current charge level.
Potentially the Alternator may also vary output voltage depending on motor speed (I know little about alternators).

Check to see yours does not sometime operate at ≥15v using a multimeter.
If it does, then it is likely you have destroyed the LEDs.

You could also check this by testing if the LEDs still work if you power them with a more trustworthy power supply, Eg a Mains-DC adaptor you have checked with a multimeter -- or if you have access to a lab regulated voltage supply, that is ideal.

The other option is a break in the wire.
This must be occurring at one of the ends, before any of the lights, as they are in parallel, so if the break was in the middle, some lights would still work.

Alternatively  you have managed to separately break a wire in each group of 3, up to the point where there is a break in the series connections between groups.



Some notes I used while working this out:

WSFS-NW180-BK LED Light strip
is made of 3528SMD LEDs

As it can be cut into subsections so long as each subsection contains 3 LEDS,
this would indicate that the circuit is made of parallel groups of 3 in series, 
looking closely at this picture I believe there is a resistor in there, but I can't make out the numbers, so don't know the resistance.







simulate this circuit &ndash; Schematic created using CircuitLab

So since you have groups of 3 in series, you have a voltage divider situation.
We can tell that  \$V_{LED} &lt; \frac{V_{supply}}{3}\$

According to the sale website the strip is rated for \$9 \le V_{supply} \le 14.8 VDC \$

According to the Datasheet for the white LED, to operate \$2.8 \le V_{LED} \le 3.6\$