I force your question work. but it's so ugly. I am not recommend you do this. but give your idea.
the idea is using one tooltip open/close event to control other tooltips programmatically.
please see jsfiddle example :jsfiddle
$('li').tooltip({
track: true,
open: function( event, ui ) {
$('input').tooltip('open');
},
close: function( event, ui ) {
$('input').tooltip('close');
}
});
$('input').tooltip({
items: '.error',
position: {my: 'left bottom-15', at: 'left top', collision: 'flipfit'},
track: true,
open: function( event, ui ) {
$('li').tooltip('open');
},
close: function( event, ui ) {
$('li').tooltip('close');
}
});