Incandescents don't generally care if its AC or DC... I think you'd be fine running it off the raw output from the transformer.

And even more: The incandescents are especially sensitive for overvoltage, so the 16..18V would kill them within very short time.

However if you want to control many of them individually from e.g. some micro or so (any chaser, sequencer, or similar effects), the AC supply makes that a bit more difficult: The triacs have too high voltage drop (2..3V) for a 12V system, while the MOSFETs work only with one polarity. So yu would have to use either electromechanical relays (limited life, when frequently flashing), or a power MOSFET based SSRs (those rated for DC, but both polarities). But those are rather expensive. Or design the SSRs yourself: Use MOSFETs in "antiseries pairs" (common source, one drain is one terminal of the resulting switch, other is the other terminal of that switch), but the driving circuit would be a bit more complex (however it wont be that much expensive, if you are able to handle the extra complexity)...

If you want solid state relays, they can be costly, but if you look on aliexpress and are willing to wait the 6 to 12 weeks they take to get in the mail they are about 10% of the cost of most major parts suppliers like Digi-key..

If you want solid state relays, they can be costly, but if you look on aliexpress and are willing to wait the 6 to 12 weeks they take to get in the mail they are about 10% of the cost of most major parts suppliers like Digi-key..

But you have to order the "DC" types (by far less common), so the MOSFET based, with switch side rating of not much more than 60VDC (otherwise the Ron would be too high). The standard ones are triac based and that has way too high voltage drop for the 12V supply.

For up to about 0.5A per channel e.g. AQY212S should be suitable.
For a bit higher current per channel, you may directly parallel multiple of these units (it is a MOSFET, so the current will balance pretty well, assume control is common, so the control LEDs in series).

Not bad on Aliexpress they are only $0.54 each in a lot of twenty so $11.50 with free shipping, so you get twice as many for $5 less and Ebay wants money to ship them so you really save $10 and you get twice as many so they are about 1/4 the cost and Alipay offers all the same protections you get with Ebay, And I've used it before and got my money back faster then ebay..