This is one of the situations where you should pick up the phone and call JBL support. They will be able to give the authoritative answer.
I did notice that there was an "anonymous" posting on that JBL-website with the same question, and it would be likely that that was you posting it. Still I would advise to pick up the phone and call them, then get them to send more info, such as wiring diagrams, over by email or any other form of communications.
The following at your own risk:
Option 1: Parallel the inputs:
You can connect both inputs in parallel (red-to-red, black-to-black). It is highly likely that the overal impedance will lower to 4 Ohm, or near to 4 Ohm. Obviously without more details on the (summing-)filter we cannot say for sure.
The Wattage of the speaker would be reated 80 Watts at 8 Ohm, while it is likely that we have now lowered the impedance of the speaker to 4 Ohm, I would advise you not to drive it with more than 80 Watts on 4 Ohm. This as there is no further details on the website. (again this is where JBL support comes in!)
You need to be careful with the amplifier you use, many amplifiers will deliver one Wattage at 8 Ohm, and a higher Wattage at 4 Ohm. This could mean that you overload the speaker. Most amplifiers now-a-days are capable of handling 4 Ohm, the risk of "burning-out" the amplifier is less. However it is good to check the manual of your amplifier.
Option 2: Wire only one side:
Only connecting one side is indeed only using one of the tweeters (as far as I understand the function of this speaker), however you do not have any of the risks of any other option. By doing this, it is simply an 8 Ohm / 80 Watts speaker.
The position of the tweeter may disperse the sound in one particular direction or area, this you will need to experiment with. E.g. connect one side, test, then connect the other side, and test again. The dispersion of high-frequencies may determine the mounting-position in the room and which side-connection of the speaker .
If JBL-support does not help you any further, this would be my preferred option, as it does not introduce any risk.
Option 3: connect in series:
I am only listing this option for completeness of the answer
In series you connect red-to-black, then feed red-one-side, black-the-other-side.
This is the most risky option, while you might think that this is possible to raise the impedance to 16 Ohm. Which would be a logical conclusion, it may or may not be the case. This depends on the (summing-)filter circuitry, which we do not know. As the filter is a "summing-filter" which summs the low-end from both ends to a single woofer, connecting in series may introduce a short !!! This will damage your amplifier, and possible the speaker.
I would NOT do option 3
Summary, what I would do:
- Call JBL support to get more info and/or their preferred wiring diagram, then stick with this
- If 1. doesn't yield any results, go with option 2, and only connect one side. I would experiment with which side to connect, and experimentally determine the optimum mounting location in the room.