I can't for the life of me find what kind of guitar they both used around 1984, Its green , kind of explorer shaped, with explorer like headstock, white triangular shape pickguard, You can see Brad Whitford using it in Let the Music do the Talking, Video...Oh and it's Not an Explorer....This is driving crazy! I have to find one!!
Looks like an explorer to me, probably it's a copy or one of those 80s gibson attempts to make some classic designs look cool for that era

Ibanez SZ320
Ibanez RG450
Ibanez SC620
Bc Rich Warlock 7 String


Digitech Whammy 4
Line 6 PodXT Live


Line 6 Flextone 2
my only contribution is to add that Perry has a fantastic sig. Gibson... never seen him with an explorer style one
Gibson SG
Ibanez RGR420ex
Marshall JTM30
Slash SW95 Crybaby
Boss DS1/DD7
Digitech Bad Monkey

It looks as though it has the styling of a Danelectro....It's not quite the shape of an Explorer..........You tube has a vid of the song Three mile smile, Reefer headed woman, 1984, Back in the Saddle tour where Perry uses it, It's a better look there but I still can't find out who mkes it!! I've searched everywhere and I thought I knew all about the gear they use?!!
adding to this
but does anyone know anything about the guitar used in the walk this way video by perry
it looks awesome
'And after a while, you can work on points for style.
Like the club tie, and the firm handshake,
A certain look in the eye and an easy smile.'

'You have to be trusted by the people that you lie to,
So that when they turn their backs on you,
You'll get the chance to put the knife in.'