Hi Staffdriver, I have had in my time, several Honeysuckles that have not flowered, Frankly I have no idea as to why some of mine send out the most delecate perfumed flowers, some of these plants (all Different types of Honeysuckle) dont have perfume but flower there hearts out, the only thing I gan think of is they are growing in the wrong soil / place / too shaded / not enough moisture at roots, I could go on but the ones that do perform for me are growing in dappled shade, left to scramble twine in there own direction BUT, they are NOT in a flower bed smothering other plants.
Honeysuckles are also knows as Woodbind, Wood = woodland plants AND Bind = they bind around any structures they come into contact with.
IF you look up Honeysuckle in any garden books it will tell you to grow these plants in Dapple shade, not darkness and not in full sun, IF growing up or into tree Ect, make sure the roots are set a few feet away from a structure /tree tied to a cane and slope this cane towards the tree / structure, the reason for this is, IF climbing plants are grown (roots) less than a foot away from wall / tree, the soil gets so little water that the Honeysuckle cant compete for nutrients or moisture,
Dont know If any of that gives clue as to any problems you are having with your plant but I feel sure some of these problems will be why your plant is not flowering,
What you can do is Hack half your plant down by pruning it, this will help untangle a lot of dead branches, old damaged branches and then add a good 4-6 inches of humus about a foot and half around the root area and this will give some feed, some moisture retention and enrich the depleted soil, fork this into the top soil but lightly as you go as you dont want to damage the roots, water well and keep an eye out to make sure the soil is not bone dry after a week or so, because these plants grow naturally on the outskirts of woodland this alone tells you this area will be a little damper and a bit shaded but not as shaded as if it was in mid woodland where the tree canopy would give even more shade when the tree's are in full foliage.
You could also add a multi purpose feed at the time of your humus mulch just to give the chopped up plant a good boost, always go by the dose of feed on packet as too much can burn plant roots, always water after feeds that are dry as in granules, or use feeds that can be watered into the soil around the roots.
Hope this helps a bit Staffdiver and it's difficult to try establish the problem when you know little about how old the plant is, what type of honeysuckle you have and in-fact, is it a honeysuckle.
Good luck and best regards.
Yes, I would do it now as soon as there are tiny buds (leaf formation) on the stems /branches, don't be surprised of there are no flowers yet again this year but because you don't know how old, type or flowering season of your plant / shrub, I think next year you should see better results, if not, then by late winter, try get rid as I doubt IF it will still want to flower, Nature sometimes gives us a dud plant, we call them blind plants as they get loads of foliage but for some reason, no flowers, I always herd the fraze, growing blind.
I know my brother planted an apple pip that grew into a sapling, then a tree and then it almost reached the roof, after about 15-20 years, the tree actually flowered so you never know, unless someone can tell you what type of honeysuckle you have, then just never say never eh !!!!
I was given a honeysuckle years ago and never seen any flowers however a couple of years ago I found tiny little dark red flowers all along the stems, not one of the most attractive plants I have to admit but it must have been flowering for years and never noticed it.
Good luck. WeeNel.