To enable back/home button on custom toolbar and add click listener on it use bellow technique.

Toolbar toolbarTop = (Toolbar) findViewById(R.id.toolbar_top);
setSupportActionBar(toolbarTop);
/*getSupportActionBar().setDisplayShowHomeEnabled(true);
getSupportActionBar().setIcon(R.drawable.ic_action_home);*/

toolbarTop.setNavigationIcon(getResources().getDrawable(R.drawable.ic_action_home));
toolbarTop.setNavigationOnClickListener(new View.OnClickListener() {
    @Override
    public void onClick(View v) {
        Intent homeInt = new Intent(SearchResult.this, Search.class);
        startActivity(homeInt);
        finish();
    }
});

🙂