Question is - does the main rocket motor ignite right afterwards?

If you've watched the videos of an SM-2/3/6 launch there is a very small delay between the separation of the Mk-72 booster and the Mk-104 sustainer firing (Just enough of a delay to get sufficient clearance between the booster and the missile's boat-tail).

And once ignited, is its thrust constant or does it have some sort of boot-sustain configuration as well?

The Mk-104 DTRM sustainer has a boost/sustain burn configuration (Dual Thrust Rocket Motor).
 
if 6 seconds for the booster is true, and if missile's max velocity with the booster is anywhere between Mach 3.5 and 5 - then after those 6 seconds the missile should be roughly at 6000 meters of altitude. If the missile goes up completely vertically. So, with some horizontal movement, perhaps closer to 5000 meters? And then the booster is jettisoned right in the 7th second - that seems logical.
Question is - does the main rocket motor ignite right afterwards? And once ignited, is its thrust constant or does it have some sort of boot-sustain configuration as well?
I always wondered, if the missile would not accelerate right away after booster separation, using its main motor, how quickly would it really shed speed? Would it reach like 10 km in altitude while still going over mach 2?

Looks like maybe a fraction of a second? It's not immediate though (though I suppose below could be a test of the booster, with an inert upper stage):

separ2.jpg
 
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Army doubles IBCS development funding in new five-year plan; ties in F-35, THAAD, more​

By Jason Sherman / April 10, 2024

The Army is doubling funding in its updated five-year budget plan for the Integrated Battle Command System in an effort to expedite development of software needed to integrate a list of new sensors, including the F-35 Joint Strike Fighter, the Terminal High Altitude Area Defense system, the Remote Interceptor Guidance-360 and more. The Army’s fiscal year 2025 budget request proposes $2.1 billion for system development and demonstration funding over five years, a substantial increase compared to the FY-24 five-year plan...

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