Find largest product of longest subsequence between min and max

Jelly, 15 bytes

NMpMr/€LÐṀịµP€Ṁ

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How?

NMpMr/€LÐṀịµP€Ṁ - Main link: list of integers, L
           µ    - links to the left as a monadic chain with argument L
N               - negate elements of L
 M              - indexes of maximal elements (i.e. indexes of minimal elements of L)
   M            - indexes of maximal elements of L
  p             - Cartesian product of the min and max indexes
     /€         - reduce each list (all of which are pairs) with the dyad:
    r           -     range(a,b)  (note if a>b this is [a,a-1,...,b])
        ÐṀ      - filter keeping those with maximal
       L        -     length
          ị     - index into L (vectorises)   (get the values)
            P€  - product of a list for €ach
              Ṁ - maximum

Perl 6, 108 bytes

{max ([*] $_ for .[.grep(+.max(+*)) with (for .min,.max,.max,.min {.first($^a,:k).. .first($^b,:k,:end)})])}

Jelly, 14 bytes

.ịạ/;L;P
ẆÇ€ṀṪ

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How it works

ẆÇ€ṀṪ     Main link. Argument: A (array)

Ẇ         Window; generate all substrings of A.
 ǀ       Map the helper link over the substrings.
   Ṁ      Take the maximum.
    Ṫ     Tail; select the last element.


.ịạ/;L;P  Helper link. Argument: S (array / substring)

.ị        At-index 0.5; select the last and first element of S.
  ạ/      Reduce by absolute difference.
    ;L    Append the length of S.
      ;P  Append the product of S.