
LordKailas |

As a DM you can ignore the requirements of a template. Just know that it isn't the norm.
IMO revenent should be a template and if you don't mind going to other game systems you could always use the revenent template from d20 modern and just apply it to the construct of your choice.
If you want to stay within pathfinder. You could take a construct and give it the Haunted Construct or Mummified Creature template. Alternatively you could take the revenent and give it the Taxidermic or Walking Weapon template.
It should be noted that out of all of the suggestions here only Haunted Construct strictly follows the rules.

Meirril |
Mainly because constructs can't raise as undead because they were never alive to begin with? I mean if you want to make it go ahead, but seriously what is next? An intelligent magic item comes back from the dead to get revenge against the guy that broke it? A wish thinks its potential has been squandered and will seek to upstage its caster by reincarnating as his rival? The fourth wall will hire a group of assassins to seek revenge for being broken consistently by several of the PC?

The Sideromancer |
Mainly because constructs can't raise as undead because they were never alive to begin with? I mean if you want to make it go ahead, but seriously what is next? An intelligent magic item comes back from the dead to get revenge against the guy that broke it? A wish thinks its potential has been squandered and will seek to upstage its caster by reincarnating as his rival? The fourth wall will hire a group of assassins to seek revenge for being broken consistently by several of the PC?
There are ways for a living being to become a construct, and there are constructs powered by energy that could be used for living beings (there are also constructs with brains in jars so they can take feats, but that's a little tangential). It may not be powered by negative energy, but experiencing cessation of existence in the kind of way I'm imagining happened here doesn't seem like it'd let any intelligence rest in peace (for reference, this would be having your entire artificial species wiped out entirely so one man could save face).