Some great advice here from some experienced professionals already.
I agree completely, and won't repeat what they say.
Whether you stand a chance depends very much on your area and partly how rough/tough the secondary is! But generally secondary TA jobs are not terribly desirable, for some of the reasons mentioned already, so your lack of specific experience and training will not necessarily be a barrier.
Our school would hesitate to employ someone with no recent experience of secondary schools. But you would strengthen your application immensely if you arranged now to go and spend a day or two in a local school just observing teachers or shadowing a TA. Most schools are very happy to arrange this sort of thing - but it may take some perseverance with the switchboard/reception, to get put through to the relevant person!
I applied for a job as a cover supervisor in secondary from a similar position to you: No relevant experience, no qualifications. I'd had a career break of 6 years for the boys, and then only worked part time for a couple of years.
The fact that I'd gone out and arranged some experience in a secondary school to support my application really impressed them. And 4 years on (or is it 5? I can't remember!), I'm still there. And most of the time I enjoy the work.