Spades - is the rule "Second hand plays low, Third hand plays high" important?
Contract Bridge (whether Rubber or Duplicate) is a similar game to Spades but with greater information available to players do to the assets of Dummy being known to all. This makes card play in Bridge a true science. However many sound lessons can still be gleaned for use in other trick-taking games such as Spades, Hearts, Euchre and Whist.
Multiple National Champion Richard Pavlicek discusses many aspects of Second hand play here. The main exceptions to the guide of Second Hand Low are:

With at least three honours where at least two are touching, play the highest of the touching honours. This is generally the same card one would lead as First Hand to open the suit.

Cover an honour led with your highest card if (a) you have two or more cards higher or (b) it is the second or subsequent round of that suit being led by an honour from First Hand.

From a strategic standpoint it is desired to win the trick (a) to lead trumps (Spades obviously in Spades); (b) to provide partner with a ruff before trumps are drawn; or (c) with a doubleton to unblock the suit and provide partner with a count in the suit.

With holdings of only small cards there is great strategic and tactical value to agreeing with partner to play a remainder-count echo where (a) the lowest card is played from a remaining odd number of small cards; (b) the highest card is played from a doubleton remaining; and (c) the second highest card is played from a 4- or 6-card holding. When both partners have learned to read these count signals in building a complete count of the hand, some esoteric end-plays become accessible in the later tricks.


Numerous examples of how these guidelines assist in maximizing a partnership's rick-taking potential are readily available on the Internet's many Contract Bridge sites, usually under the main heading of Defensive Card Play such as here (again) by Richard Pavlicek.
Terminology:

Ruff - When out of the suit led, playing a trump (ie a Spade) in an attempt to win the trick.

Honour - While Honours are normally regarded as the cards Ten through Ace, for the purposes of this analysis, the Nine should be regarded as an honour also.

Touching Honours - Two cards of the same suit, both honours, of adjacent rank such as AK, KQ, QJ, JT, or T9.

Doubleton - A two-card holding in a suit. Depending on context this might refer to either the original holding of the suit, or to the remaining holding in the suit. Likewise Singleton and Tripleton for 1-card and 3-card holdings in a suit.

Echo - The playing of small cards to the first two rounds of a suit such that the card played on the first round is higher than that played on the second. It is usually done with an even number of cards in the suit to assist partner in counting the hands around the table.
In the Trump suit (always Spades playing Spades) partnerships may find it useful to reverse the signal (echoing with three or five) to explicitly signal possession of an additional Trump (ie Spade) and an ability to ruff in a side suit.


Note on echoing:
While the value is undoubtedly reduced when both Dummy is unexposed and Partner is blind to the meaning, my recommendation would be to still make these plays. They will cost little, and have tactical value in and of themselves - most particularly playing second highest from a 4-card holding (led by 0 or 1 honour) on the first round.
Note on importance of these guidelines
In my university days I shared a house with a group that enjoyed the 3-player Whist variant Nine-Five-Two (or Sergeant Major). It employs a cascading scoring system that results in better card play early on improving one's hand in subsequent deals. My deeper understanding of card combinations and greater discipline at counting the hand was worth perhaps 1/4 of a trick each hand - with the result that I won almost twice my share of games, and virtually 100% of games that lasted longer than 7 or 8 deals. Yes, better card play will very much influence one's success in trick-taking card games.