There is a problem with that solution. "Constant" really only is a modifier on Sun duration (or similar, e.g. repeating spells). If the anvil is out of range, then the spell will still last until sunrise/sunset.
I differ with you here. I see constant as it's own duration that is computed useing sun duration rather than a modified sun duration.
But taking your answers (which are completely conssistant with the book) would you allow a duration concentration, item maintains concentration, evironmental trigger by sunrise sunset, non-flickering enchantment for 2 or 3 levels more than a flickering enchantment (as a non-standard duration)?
Weren't you the one who was lamenting the lack of breakthroughs in the books? 
Well, that sure does smell like a Minor Breakthrough to me, or something that someone with Harnessed Magic could pull off at no extra cost based on the Sun/constant approach.
If the breakthrough is already out there, all it would take to learn how to do it could be to investigate an item with such an effect in it, or craft one with a lab text (analogous with learning a spell).
I'm tempted to ask for a full +5 levels, but +2 or +3 is probably enough, given that we'd already have added 9 levels on top of the effect's level, as well as at least matched Sun/constant. Going beyond that wouldn't really make it worth the hassle.
I'd do it as a non-standard duration. Breakthrough shmakethrough 
But I'd be ok with your choice in a game as well. It just isn't my favorite answer.
I was looking for more breakthroughs in the published material.
I rather like the idea of the necklace flickering. I can see a magus flying through the air, unaware of what time it is, then taking a crash landing like Wile E. Coyote. 