Would I be correct t in saying the different types of LED will make no difference as they are connected in parallel?
Yes and No.
LED's require some kind of driving circuit or protection.
Cheap setups use resistors, better setups (usually) use some kind of current control circuit.
If these devices are used with the LEDs, then you can mismatch and mix your LED modules in parallel and be fine. They are usually included for automotive LED lighting
inside the enclosure.
If this device is provided as an 'external' required accessory like a transformer, then you must carefully follow the installation instructions. Mixing LEDs
after this device is a bad idea. (This device is usually built in to those types of LED enclosures though. An example of when they are not is kitchen LED puck/strip lighting requiring a transformer)
Additionally, if the manufacturer skipped using these things it could be very bad and they are most likely burnt out already. This is unlikely though as the seller would be long out of business.
Those lamps appear to be sealed as well, so taking the amber housing off wont work...
I hate to say it, but the only thing I can think of from here is clipping the wire to one of your lighting modules and testing it by itself. Perhaps the manufacturer accidentally swapped the yellow and black wires leading you to unknowingly hook them up backwards...
Was there any documentation sent with the lights? Robust products have reverse polarity protection... I'm hoping the paperwork sent with them says something about it. Either as a big No-No, or as a troubleshooting step. 'If these don't work swap polarity'.
Don't actually swap the wire while you test one of them though... it could be a very bad idea if the device does not have built in protection for it.