It's like any job, if you were a sight reading jazzer you'd be on those types of gig, you'd meet other musicians with other gigs who'd take your number and you'd get called to dep on other gigs, so on and so forth, unless you can read you are unlikely to seek out those gigs yourself to get started and even if you blagged your way into a band using your ears that would work (that's what I do now), if you made a good job of it then you might get asked for your number by other musicians, you'd then have to ask them what the deal was if they rang you in six months time, they might presume you read only to be faced with fly sh*t on the gig!
People that know me within the band and live music scene context generally know what skills I have or in this case don't have, they won't give my number to someone specifically looking for a reading player for a theatre show but will for normal pub/function/wedding stuff.