Conversion Tracking: What options are there?

I've been developing an online marketing software that will be embedded into clients' websites in order to improve conversion rate. So, I'm looking for a solution to track conversion (e.g., subscription start, demo inquiry) on websites as a third-party software vendor, but struggling which solution is best. (Obviously, I would not like to rely on other third-party tools such as Google Analytics)

So far, I found two solutions with my understanding. (Both are JS-based)

• Trigger on click: Counting CTA clicks by interrupting default click action to fetch conversion data then resuming the action.
  • Cons: Precise conversion tracking due to actual click-based system.
  • Pros: Complex setting needed if there are multiple CTA buttons inside one page.
• Trigger on page transition: Counting visits on specific pages which are shown after CTA is completed.
  • Cons: Easy setting (c.f., only specifying pages is required)
  • Pros: Inapplicable for some websites if there are no specific pages showing "action completed" (e.g., Thanks page)

It would be really appreciated if you could share other tracking options/suggest which tracking option would be better.