How could we determine that a particular transaction in which block's Merkle tree? https://blog.ethereum.org/2015/11/15/merkling-in-ethereum/ :

If the light client wants to determine the status of a transaction, it
can simply ask for a Merkle proof showing that a particular
transaction is in one of the Merkle trees whose root is in a block
header for the main chain.


Please note that image is taken from reference 1.

Verification of a Merkle path proceed from the leaf node to the Merkle
root.

As seen from the example image, we actually could not know that transaction-3 is located under that specific block and leaf-node since a light client only downloads the merkle root.
[Q] How could we determine that a particular transaction in which block's Merkle tree and Merkle tree's which leaf node? In order to determine the status of that transaction should we iterate through all blocks in the blockchain until we find the specific transaction? And when we find its block number, how could be actually determine its leaf node.
Thank you for your valuable time and help.
(1) https://blog.ethereum.org/2015/11/15/merkling-in-ethereum/
As seen from the example image, we actually could not know that transaction-3 is located under that specific block and leaf-node since a light client only downloads the merkle root


As a light client, you would be given the branch/path of the tree which corresponds to the transaction you wish to know about, not just the merkle root. By giving you the transaction itself, and the branch of the tree, it lets you verify that the transaction was indeed part of that merkle root. Otherwise there is no way to tell, it is not possible to extra transaction IDs from a merkle root without being given the tree of transactions themselves. A merkle root is just a hash, a 'summary' and commitment to the transactions, it doesn't actually contain any information.