piecewise - Identifying maximal element in a list with case distinctions

I need to create code that identifies the positions of all maximum elements of a list. I already know that if myList contains only numbers, I can do

mList={0,1}    
Position[myList,Max[myList]] 

This will return, as expected, {{2}}.

However my case is a bit more complicated because the list contains variables.

Here is an example to illustrate:

myList = {1, a};
Position[myList, Max[myList]]

This returns {}.

I fully understand that this is because none of the elements in myList matches the expression Max[1,a].

I've tried various variants of the following, to no avail:

PiecewiseExpand[Max[myList]]
Position[myList,%]

The first line returns, as expected: "1 if a<=1, a otherwise". But the second line returns {}. (Again, I understand that this is because the list elements don't match the piecewise function.)

Is there a way to change this code so that I get the following desired result:

"1 if a <=1; 2 otherwise"

(That is: I want the output to be the unevaluated conditional statement.)

Answer

posMax[list_] := Module[{pw = PiecewiseExpand[Max[list]]}, 
  If[NumericQ@pw, Position[list, pw], MapAt[Position[list, #] &, pw, {{1, All, 1}, {2}}]]]

Examples:

posMax[{0, 3, 2}]

{{2}}

posMax[{0, a}] // TeXForm

$\begin{cases} \left( \begin{array}{c} 2 \\ \end{array} \right) & a>0 \\ \left( \begin{array}{c} 1 \\ \end{array} \right) & \text{True} \end{cases}$

posMax[{0, 1, a, b}] // TeXForm

$\begin{cases} \left( \begin{array}{c} 2 \\ \end{array} \right) & a\leq 1\land b\leq 1 \\ \left( \begin{array}{c} 3 \\ \end{array} \right) & a>1\land a-b\geq 0 \\ \left( \begin{array}{c} 4 \\ \end{array} \right) & \text{True} \end{cases}$