First off - you refer to right side headlight; but, that sure looks like the left side headlight. Is the gap that you are talking about the horizontal spacing between the hood and the back edge of the headlight door? If so, look at page 23-182 of the 1991 service manual (in the electrical section, not in the body section which I referred to in that 4 year old post).
As our NSX continues to age, it will become more and more important for member to be able to service their cars. Most Acura dealers no longer employ technicians who are familiar with the NSX, as the original techs are long gone or retired. As...
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You will see that the headlight door / cover (Honda calls it garnish) is attached by four screws hidden by little covers. Remove the covers and loosen off the screws and this will allow you a small amount of freedom to move the whole cover forward or backwards, up or down and tilt it left/right - these are all small adjustments determined by the slop in the mounting holes. This is the PITA adjustment I referred to because you fiddle, drop the doors closed to check, then lift and adjust, repeat, repeat, repeat.....
If the gap is a difference in the vertical height of the door relative to the edge of the hood, first make sure that the hood height is correct. It should be flush with the fender and there is an easily accessible rubber bumper that sets the close height. This is an 'easier adjustment and is described in the body section of the service manual. If the hood height is correct or you have adjusted it to be correct and you still have a vertical displacement, then you can loosen off the four screws holding the covers in place and you should be able to adjust the covers down or up a bit as described in the previous paragraph.
Do not remove the front wheel and fender liner. There is no access to the headlight mechanism from the wheel well. Everything is done from up top.
The preceding assumes that there has been no damage to the headlight mechanism or that the body sections to which the headlight are mounted have not been the victim of a sheet metal bending incident.