tooltips missing sometimes

In DrRacket, this program:

#lang typed/racket #:no-optimize

(: plus (-> (U String Integer)
            (U String Integer)
            (U String Integer)))
(define (plus x y)
  (cond
    [(and (number? x) (number? y))
     (+ x y)]
    [(number? x)
     (string-append
      (format "~a" x)
      (format "~a" y))]
    [(string? x)
     (string-append
      (format "~a" x)
      (format "~a" y))]
    [else
     (+ x (car x))]))

shows no tooltips in the (+ x (car x)) bit. It would be nice to show something about what's going on (not just silence).

Reproduce the example in DrRacket using the provided Typed Racket program, focusing on the (+ x (car x)) expression where tooltips disappear. Trace the tooltip or type-information handling for this case and determine how the failure is reported. Done means the expression provides an informative tooltip or diagnostic instead of remaining silent.