Strange Typeable error message involving TypeInType

I originally discovered this when tinkering with #13871 (closed). This program:

{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeInType #-}
{-# LANGUAGE TypeOperators #-}
module Foo where

import Data.Kind
import Data.Typeable

data Foo (a :: Type) (b :: Type) where
  MkFoo :: (a ~ Int, b ~ Char) => Foo a b

data family Sing (a :: k)
data SFoo (z :: Foo a b) where
  SMkFoo :: SFoo MkFoo

f :: String
f = show $ typeOf SMkFoo

Fails in GHC 8.0.1, 8.0.2, and 8.2 (after applying D3671) with a rather unsightly error message:

GHCi, version 8.3.20170624: http://www.haskell.org/ghc/  :? for help
Loaded GHCi configuration from /home/rgscott/.ghci
[1 of 1] Compiling Foo              ( Foo.hs, interpreted )

Foo.hs:19:12: error:
    • No instance for (Typeable <>) arising from a use of ‘typeOf’
    • In the second argument of ‘($)’, namely ‘typeOf SMkFoo’
      In the expression: show $ typeOf SMkFoo
      In an equation for ‘f’: f = show $ typeOf SMkFoo
   |
19 | f = show $ typeOf SMkFoo
   |            ^^^^^^^^^^^^^

I'm not sure what this mysterious <> is, but I'm pretty sure it shouldn't be making an appearance here. (See also #13780 (closed), where <> also makes a surprise guest appearance.)

Trac metadata

Trac field	Value
Version	8.0.1
Type	Bug
TypeOfFailure	OtherFailure
Priority	normal
Resolution	Unresolved
Component	Compiler (Type checker)
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