I do not know where the cruise control is located Mazda Miata

Question edited for clarity.
Question moved to model category.

Yes, you are correct, disconnecting the fuse box has broken the pairing between the key and the immobilizer system. Did you remove the main connection plugs to the fuse box? My thought is that those connectors have never been removed since the car was built and breaking a remaking the connection, you might have some connections that as not as good as they should be. Pull the connectors again and give them a good spray with electrical contact cleaner (that is NOT WD40). Then reconnect.

There is various ideas on resetting the Immobilizer here.

https://www.google.com/search?q=mazda+miata+immobilizer+system+reset

Or a Mobile Auto Locksmith

https://www.google.com/search?q=mobile+auto+locksmith+near+me

Just for fun, here are the Fuse Box locations and diagrams. They have changed over the years, and as you didn't state the year, here is all of them.

Mazda MX-5 Miata (NA; 1989-1997) fuses

Fuse Box Diagrams https://fuse-box.info > mazda > mazda-mx-5-miata-na...

Here you will find fuse box diagrams of Mazda MX-5 Miata 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, get information about the location of the fuse ...

Mazda MX-5 Miata (ND; 2016-2023) fuses

Fuse Box Diagrams https://fuse-box.info > mazda > mazda-mx-5-miata-nd...

Fuse box diagram (location and assignment of electrical fuses) for Mazda MX-5 Miata (MX5) (ND; 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023).

Leave this to the experts, very complicated testing with a special electronic scan tool must be done.

Check the fuses in your vehicles fuse box.

Did they tell you what it needed ? Was it the speed sensor in the transaxle ?

probably not. Once you find and correct the problem then you will know if it was related or not. Check the fuse and the brake switch, that's the most common things.

That toggle switch is for the security system. That year miata never came with any switches for the soft top of any kind. Most likely that is an aftermarket alarm system. Most factory alarm systems do not come with a toggle switch.

Mazda Miata/MX5 Service and Repair Manuals is good for this kind of thing, has all Miata manuals ever.

Simply look up the VIN code and you will get the year and location it was manufactured.

se if egr is controled by vacium or electric
if it is by vacium then locate the egr solenoide and make sure it has vacium in one hose w/ engine runing if it does then replace solenoide