The easiest ones, you can make with some thin nichel-chrome wire (you can also mangle a 200 / 300 ohm 15W ceramic resistor, if you don't find it in more easy way, but you can find it also in heathers, heat wires, old toasters, and so on) and some pieces of telephone cable (2 wires, single core copper wire)
take also the fuses of some poppers (petards, whatever you call them), the ones that are made with paper and black powder, and cut or bend them approximatively 8 or 10mm lenght, you need 10 or 15 pieces for each ignitor, the number is not important, but, more they are, better they burn
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For more indications, look also the images.
Type 1, coaxial mount ..... just put the fuse pieces and the wires together in the way you see in the draw, keep them together with 10 or 12 turns of ni-cr wire (thin one), or 5 / 6 turns, (if you only found the 0,5mm strip from the toasters, instead thin wire), and fix the extremities of the ni-cr wire to the extremities of the phone cable wires as shown (remember that you can't solder the wires, so for fix it, just turn it around the copper wire some turns, then bend the copper wire and squeeze it, as in the pic).
About the number of turns of ni-cr wire, make some experiments for get the better number of turns for the wire that you found, cause i can't know what type of wire you can found.
type 2, match shape, just keep the phone cables as shown, putting the fuse pieces only around the long wire, and do the same as in the previous one.
Type 3, waterproof ..... take some of the little lamps that you usually use for christmas tree decorations, and break their points, without break the rest ..... fill the class tube half to 3/4 with black powder (you can make it yourself or use the one in the paper fuses, as preferred), then close the hole at the top with hard glue (2-components epoxy resin, the 5 minutes type, is enough, be sure to place a tear of it on the top but not let it go on the powder, nor turn the lamp upside down til the resin is completely dry)
For ignite fuses and powders, they can be used also in this form, but for be sure to ignite paper and other for a camp fire, one more passage is better (for the 2 types with the fuses, i mean ..... type 3 is better for blow other powders)
If you have matches, take away the cap (the ignition parts), of some of them, say, 50 or 100, if you have patience ..... put all the caps (without the wood part ! ) in a mortar or similat, and wet them with water and acetone (yes, water AND acetone together) ..... stir and mix til the caps are all melted in a paste (adding some acetone when it evaporate, if needed), and when it's all of the consistence of a dense paste, cover the igniters made with the fuses and ni-cr wires with that paste, then left dry completely ..... this make a better flame when they ignite, and permit you to use them also for start paper under the wood for a firecamp, or if you use some paraffine or "barbecue igniter" fluid, or similar, on fabric, then you can weap the igniter in some layer of pliofoil (food conservation plastic, domopak, whatever you call it), and then wrap around it the soaked fabric, and it still ignite all, where instead, with just the fuses, it can also not be enough.
By the way, if you're not sure about how to manage chemicals, is enough that you take the powder and pieces of 20 or 30 matches caps (at this point you can also just cut away them, don't care if there's also the wood in the caps), and pack them all around the fuse packet with 5 or 6 turns of that plastic foil, keeping all tight together, then wrap the sides on the wires and roll them with cotton wire or similar, for keep all in place.
Anyway, as suggestion, i still say you to use 2 or 3 in parallel, instead just one ..... remember Murphy's laws
And make also some experiments, about the turns of the wire of ni-cr, cause i can't know what one you can find there, and can be diffrtrnt from mine.
@ Bionic Badger: if you use a circuit with ldr and ignitors, you don't need to use a powerful laser, also a 10mw or similar is enough ..... but you need good sight and firm hand, anyway
..... and if instead you just want to do the scene, and have already one of those remote control igniters, just aim the fireplace with your 50mW greenie and push the button of the remote control unit in your pocket .....